Álgebra Exemplos

$f (x) = \frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9$

Etapa 1

Escreva $f (x) = \frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9$ como uma equação.

$y = \frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9$

Etapa 2

Alterne as variáveis.

$x = \frac{{(y - 7)}^{\frac{1}{5}}}{7} + 9$

Etapa 3

Resolva $y$ .

Toque para ver mais passagens...

Etapa 3.1

Reescreva a equação como $\frac{{(y - 7)}^{\frac{1}{5}}}{7} + 9 = x$ .

$\frac{{(y - 7)}^{\frac{1}{5}}}{7} + 9 = x$

Etapa 3.2

Simplifique $\frac{{(y - 7)}^{\frac{1}{5}}}{7} + 9$ .

Toque para ver mais passagens...

Etapa 3.2.1

Para escrever $9$ como fração com um denominador comum, multiplique por $\frac{7}{7}$ .

$\frac{{(y - 7)}^{\frac{1}{5}}}{7} + 9 \cdot \frac{7}{7} = x$

Etapa 3.2.2

Combine $9$ e $\frac{7}{7}$ .

$\frac{{(y - 7)}^{\frac{1}{5}}}{7} + \frac{9 \cdot 7}{7} = x$

Etapa 3.2.3

Combine os numeradores em relação ao denominador comum.

$\frac{{(y - 7)}^{\frac{1}{5}} + 9 \cdot 7}{7} = x$

Etapa 3.2.4

Multiplique $9$ por $7$ .

$\frac{{(y - 7)}^{\frac{1}{5}} + 63}{7} = x$

Etapa 3.3

Multiplique os dois lados da equação por $7$ .

$7 \frac{{(y - 7)}^{\frac{1}{5}} + 63}{7} = 7 x$

Etapa 3.4

Simplifique o lado esquerdo.

Toque para ver mais passagens...

Etapa 3.4.1

Cancele o fator comum de $7$ .

Toque para ver mais passagens...

Etapa 3.4.1.1

Cancele o fator comum.

$7 \frac{{(y - 7)}^{\frac{1}{5}} + 63}{7} = 7 x$

Etapa 3.4.1.2

Reescreva a expressão.

${(y - 7)}^{\frac{1}{5}} + 63 = 7 x$

Etapa 3.5

Subtraia $63$ dos dois lados da equação.

${(y - 7)}^{\frac{1}{5}} = 7 x - 63$

Etapa 3.6

Eleve cada lado da equação à potência de $5$ para eliminar o expoente fracionário no lado esquerdo.

${({(y - 7)}^{\frac{1}{5}})}^{5} = {(7 x - 63)}^{5}$

Etapa 3.7

Simplifique o expoente.

Toque para ver mais passagens...

Etapa 3.7.1

Simplifique o lado esquerdo.

Toque para ver mais passagens...

Etapa 3.7.1.1

Simplifique ${({(y - 7)}^{\frac{1}{5}})}^{5}$ .

Toque para ver mais passagens...

Etapa 3.7.1.1.1

Multiplique os expoentes em ${({(y - 7)}^{\frac{1}{5}})}^{5}$ .

Toque para ver mais passagens...

Etapa 3.7.1.1.1.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

${(y - 7)}^{\frac{1}{5} \cdot 5} = {(7 x - 63)}^{5}$

Etapa 3.7.1.1.1.2

Cancele o fator comum de $5$ .

Toque para ver mais passagens...

Etapa 3.7.1.1.1.2.1

Cancele o fator comum.

${(y - 7)}^{\frac{1}{5} \cdot 5} = {(7 x - 63)}^{5}$

Etapa 3.7.1.1.1.2.2

Reescreva a expressão.

${(y - 7)}^{1} = {(7 x - 63)}^{5}$

Etapa 3.7.1.1.2

Simplifique.

$y - 7 = {(7 x - 63)}^{5}$

Etapa 3.7.2

Simplifique o lado direito.

Toque para ver mais passagens...

Etapa 3.7.2.1

Simplifique ${(7 x - 63)}^{5}$ .

Toque para ver mais passagens...

Etapa 3.7.2.1.1

Use o teorema binomial.

$y - 7 = {(7 x)}^{5} + 5 {(7 x)}^{4} \cdot - 63 + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2

Simplifique cada termo.

Toque para ver mais passagens...

Etapa 3.7.2.1.2.1

Aplique a regra do produto a $7 x$ .

$y - 7 = 7^{5} x^{5} + 5 {(7 x)}^{4} \cdot - 63 + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.2

Eleve $7$ à potência de $5$ .

$y - 7 = 16807 x^{5} + 5 {(7 x)}^{4} \cdot - 63 + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.3

Aplique a regra do produto a $7 x$ .

$y - 7 = 16807 x^{5} + 5 (7^{4} x^{4}) \cdot - 63 + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.4

Eleve $7$ à potência de $4$ .

$y - 7 = 16807 x^{5} + 5 (2401 x^{4}) \cdot - 63 + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.5

Multiplique $2401$ por $5$ .

$y - 7 = 16807 x^{5} + 12005 x^{4} \cdot - 63 + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.6

Multiplique $- 63$ por $12005$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 10 {(7 x)}^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.7

Aplique a regra do produto a $7 x$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 10 (7^{3} x^{3}) {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.8

Eleve $7$ à potência de $3$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 10 (343 x^{3}) {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.9

Multiplique $343$ por $10$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 3430 x^{3} {(- 63)}^{2} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.10

Eleve $- 63$ à potência de $2$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 3430 x^{3} \cdot 3969 + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.11

Multiplique $3969$ por $3430$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} + 10 {(7 x)}^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.12

Aplique a regra do produto a $7 x$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} + 10 (7^{2} x^{2}) {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.13

Eleve $7$ à potência de $2$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} + 10 (49 x^{2}) {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.14

Multiplique $49$ por $10$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} + 490 x^{2} {(- 63)}^{3} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.15

Eleve $- 63$ à potência de $3$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} + 490 x^{2} \cdot - 250047 + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.16

Multiplique $- 250047$ por $490$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 5 (7 x) {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.17

Multiplique $7$ por $5$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 35 x {(- 63)}^{4} + {(- 63)}^{5}$

Etapa 3.7.2.1.2.18

Eleve $- 63$ à potência de $4$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 35 x \cdot 15752961 + {(- 63)}^{5}$

Etapa 3.7.2.1.2.19

Multiplique $15752961$ por $35$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x + {(- 63)}^{5}$

Etapa 3.7.2.1.2.20

Eleve $- 63$ à potência de $5$ .

$y - 7 = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436543$

Etapa 3.8

Mova todos os termos que não contêm $y$ para o lado direito da equação.

Toque para ver mais passagens...

Etapa 3.8.1

Some $7$ aos dois lados da equação.

$y = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436543 + 7$

Etapa 3.8.2

Some $- 992436543$ e $7$ .

$y = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536$

Etapa 4

Substitua $y$ por $f^{- 1} (x)$ para mostrar a resposta final.

$f^{- 1} (x) = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536$

Etapa 5

Verifique se $f^{- 1} (x) = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536$ é o inverso de $f (x) = \frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9$ .

Toque para ver mais passagens...

Etapa 5.1

Para verificar o inverso, veja se $f^{- 1} (f (x)) = x$ e $f (f^{- 1} (x)) = x$ .

Etapa 5.2

Avalie $f^{- 1} (f (x))$ .

Toque para ver mais passagens...

Etapa 5.2.1

Estabeleça a função do resultado composto.

$f^{- 1} (f (x))$

Etapa 5.2.2

Avalie $f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)$ substituindo o valor de $f$ em $f^{- 1}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3

Simplifique cada termo.

Toque para ver mais passagens...

Etapa 5.2.3.1

Para escrever $9$ como fração com um denominador comum, multiplique por $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9 \cdot \frac{7}{7})}^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.2

Combine $9$ e $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + \frac{9 \cdot 7}{7})}^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.3

Combine os numeradores em relação ao denominador comum.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 {(\frac{{(x - 7)}^{\frac{1}{5}} + 9 \cdot 7}{7})}^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.4

Multiplique $9$ por $7$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 {(\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7})}^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.5

Aplique a regra do produto a $\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{5}}{7^{5}}) - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.6

Eleve $7$ à potência de $5$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = 16807 (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{5}}{16807}) - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.7

Cancele o fator comum de $16807$ .

Toque para ver mais passagens...

Etapa 5.2.3.7.1

Cancele o fator comum.

Etapa 5.2.3.7.2

Reescreva a expressão.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = {({(x - 7)}^{\frac{1}{5}} + 63)}^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.8

Use o teorema binomial.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = {({(x - 7)}^{\frac{1}{5}})}^{5} + 5 {({(x - 7)}^{\frac{1}{5}})}^{4} \cdot 63 + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9

Simplifique cada termo.

Toque para ver mais passagens...

Etapa 5.2.3.9.1

Multiplique os expoentes em ${({(x - 7)}^{\frac{1}{5}})}^{5}$ .

Toque para ver mais passagens...

Etapa 5.2.3.9.1.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = {(x - 7)}^{\frac{1}{5} \cdot 5} + 5 {({(x - 7)}^{\frac{1}{5}})}^{4} \cdot 63 + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.1.2

Cancele o fator comum de $5$ .

Toque para ver mais passagens...

Etapa 5.2.3.9.1.2.1

Cancele o fator comum.

Etapa 5.2.3.9.1.2.2

Reescreva a expressão.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = (x - 7) + 5 {({(x - 7)}^{\frac{1}{5}})}^{4} \cdot 63 + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.2

Simplifique.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 5 {({(x - 7)}^{\frac{1}{5}})}^{4} \cdot 63 + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.3

Multiplique os expoentes em ${({(x - 7)}^{\frac{1}{5}})}^{4}$ .

Toque para ver mais passagens...

Etapa 5.2.3.9.3.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 5 {(x - 7)}^{\frac{1}{5} \cdot 4} \cdot 63 + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.3.2

Combine $\frac{1}{5}$ e $4$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 5 {(x - 7)}^{\frac{4}{5}} \cdot 63 + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.4

Multiplique $63$ por $5$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 10 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.5

Multiplique os expoentes em ${({(x - 7)}^{\frac{1}{5}})}^{3}$ .

Toque para ver mais passagens...

Etapa 5.2.3.9.5.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 10 {(x - 7)}^{\frac{1}{5} \cdot 3} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.5.2

Combine $\frac{1}{5}$ e $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 10 {(x - 7)}^{\frac{3}{5}} \cdot 63^{2} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.6

Eleve $63$ à potência de $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 10 {(x - 7)}^{\frac{3}{5}} \cdot 3969 + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.7

Multiplique $3969$ por $10$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 10 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.8

Multiplique os expoentes em ${({(x - 7)}^{\frac{1}{5}})}^{2}$ .

Toque para ver mais passagens...

Etapa 5.2.3.9.8.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 10 {(x - 7)}^{\frac{1}{5} \cdot 2} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.8.2

Combine $\frac{1}{5}$ e $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 10 {(x - 7)}^{\frac{2}{5}} \cdot 63^{3} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.9

Eleve $63$ à potência de $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 10 {(x - 7)}^{\frac{2}{5}} \cdot 250047 + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.10

Multiplique $250047$ por $10$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 63^{4} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.11

Eleve $63$ à potência de $4$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 5 {(x - 7)}^{\frac{1}{5}} \cdot 15752961 + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.12

Multiplique $15752961$ por $5$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 63^{5} - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.9.13

Eleve $63$ à potência de $5$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 7 + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436543 - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.10

Some $- 7$ e $992436543$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.11

Para escrever $9$ como fração com um denominador comum, multiplique por $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9 \cdot \frac{7}{7})}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.12

Combine $9$ e $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + \frac{9 \cdot 7}{7})}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.13

Combine os numeradores em relação ao denominador comum.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}} + 9 \cdot 7}{7})}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.14

Multiplique $9$ por $7$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 {(\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7})}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.15

Aplique a regra do produto a $\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 \frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{4}}{7^{4}} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.16

Eleve $7$ à potência de $4$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 756315 \frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{4}}{2401} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.17

Cancele o fator comum de $2401$ .

Toque para ver mais passagens...

Etapa 5.2.3.17.1

Fatore $2401$ de $- 756315$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 + 2401 (- 315) (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{4}}{2401}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.17.2

Cancele o fator comum.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 + 2401 \cdot (- 315 \frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{4}}{2401}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.17.3

Reescreva a expressão.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {({(x - 7)}^{\frac{1}{5}} + 63)}^{4} + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.18

Use o teorema binomial.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({({(x - 7)}^{\frac{1}{5}})}^{4} + 4 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63 + 6 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.19

Simplifique cada termo.

Toque para ver mais passagens...

Etapa 5.2.3.19.1

Multiplique os expoentes em ${({(x - 7)}^{\frac{1}{5}})}^{4}$ .

Toque para ver mais passagens...

Etapa 5.2.3.19.1.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{1}{5} \cdot 4} + 4 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63 + 6 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.19.1.2

Combine $\frac{1}{5}$ e $4$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 4 {({(x - 7)}^{\frac{1}{5}})}^{3} \cdot 63 + 6 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.19.2

Multiplique os expoentes em ${({(x - 7)}^{\frac{1}{5}})}^{3}$ .

Toque para ver mais passagens...

Etapa 5.2.3.19.2.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 4 {(x - 7)}^{\frac{1}{5} \cdot 3} \cdot 63 + 6 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.19.2.2

Combine $\frac{1}{5}$ e $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 4 {(x - 7)}^{\frac{3}{5}} \cdot 63 + 6 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.19.3

Multiplique $63$ por $4$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 6 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.19.4

Multiplique os expoentes em ${({(x - 7)}^{\frac{1}{5}})}^{2}$ .

Toque para ver mais passagens...

Etapa 5.2.3.19.4.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 6 {(x - 7)}^{\frac{1}{5} \cdot 2} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.19.4.2

Combine $\frac{1}{5}$ e $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 6 {(x - 7)}^{\frac{2}{5}} \cdot 63^{2} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.19.5

Eleve $63$ à potência de $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 6 {(x - 7)}^{\frac{2}{5}} \cdot 3969 + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.19.6

Multiplique $3969$ por $6$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 23814 {(x - 7)}^{\frac{2}{5}} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 63^{3} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.19.7

Eleve $63$ à potência de $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 23814 {(x - 7)}^{\frac{2}{5}} + 4 {(x - 7)}^{\frac{1}{5}} \cdot 250047 + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.19.8

Multiplique $250047$ por $4$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 23814 {(x - 7)}^{\frac{2}{5}} + 1000188 {(x - 7)}^{\frac{1}{5}} + 63^{4}) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.19.9

Eleve $63$ à potência de $4$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 ({(x - 7)}^{\frac{4}{5}} + 252 {(x - 7)}^{\frac{3}{5}} + 23814 {(x - 7)}^{\frac{2}{5}} + 1000188 {(x - 7)}^{\frac{1}{5}} + 15752961) + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.20

Aplique a propriedade distributiva.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 315 (252 {(x - 7)}^{\frac{3}{5}}) - 315 (23814 {(x - 7)}^{\frac{2}{5}}) - 315 (1000188 {(x - 7)}^{\frac{1}{5}}) - 315 \cdot 15752961 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.21

Simplifique.

Toque para ver mais passagens...

Etapa 5.2.3.21.1

Multiplique $252$ por $- 315$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 315 (23814 {(x - 7)}^{\frac{2}{5}}) - 315 (1000188 {(x - 7)}^{\frac{1}{5}}) - 315 \cdot 15752961 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.21.2

Multiplique $23814$ por $- 315$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315 (1000188 {(x - 7)}^{\frac{1}{5}}) - 315 \cdot 15752961 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.21.3

Multiplique $1000188$ por $- 315$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 315 \cdot 15752961 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.21.4

Multiplique $- 315$ por $15752961$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.22

Para escrever $9$ como fração com um denominador comum, multiplique por $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9 \cdot \frac{7}{7})}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.23

Combine $9$ e $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + \frac{9 \cdot 7}{7})}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.24

Combine os numeradores em relação ao denominador comum.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}} + 9 \cdot 7}{7})}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.25

Multiplique $9$ por $7$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 {(\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7})}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.26

Aplique a regra do produto a $\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{3}}{7^{3}}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.27

Eleve $7$ à potência de $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 13613670 (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{3}}{343}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.28

Cancele o fator comum de $343$ .

Toque para ver mais passagens...

Etapa 5.2.3.28.1

Fatore $343$ de $13613670$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 343 (39690) (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{3}}{343}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.28.2

Cancele o fator comum.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 343 \cdot (39690 (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{3}}{343})) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.28.3

Reescreva a expressão.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {({(x - 7)}^{\frac{1}{5}} + 63)}^{3} - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.29

Use o teorema binomial.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({({(x - 7)}^{\frac{1}{5}})}^{3} + 3 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63 + 3 {(x - 7)}^{\frac{1}{5}} \cdot 63^{2} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.30

Simplifique cada termo.

Toque para ver mais passagens...

Etapa 5.2.3.30.1

Multiplique os expoentes em ${({(x - 7)}^{\frac{1}{5}})}^{3}$ .

Toque para ver mais passagens...

Etapa 5.2.3.30.1.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{1}{5} \cdot 3} + 3 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63 + 3 {(x - 7)}^{\frac{1}{5}} \cdot 63^{2} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.30.1.2

Combine $\frac{1}{5}$ e $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 3 {({(x - 7)}^{\frac{1}{5}})}^{2} \cdot 63 + 3 {(x - 7)}^{\frac{1}{5}} \cdot 63^{2} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.30.2

Multiplique os expoentes em ${({(x - 7)}^{\frac{1}{5}})}^{2}$ .

Toque para ver mais passagens...

Etapa 5.2.3.30.2.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 3 {(x - 7)}^{\frac{1}{5} \cdot 2} \cdot 63 + 3 {(x - 7)}^{\frac{1}{5}} \cdot 63^{2} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.30.2.2

Combine $\frac{1}{5}$ e $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 3 {(x - 7)}^{\frac{2}{5}} \cdot 63 + 3 {(x - 7)}^{\frac{1}{5}} \cdot 63^{2} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.30.3

Multiplique $63$ por $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 189 {(x - 7)}^{\frac{2}{5}} + 3 {(x - 7)}^{\frac{1}{5}} \cdot 63^{2} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.30.4

Eleve $63$ à potência de $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 189 {(x - 7)}^{\frac{2}{5}} + 3 {(x - 7)}^{\frac{1}{5}} \cdot 3969 + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.30.5

Multiplique $3969$ por $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 189 {(x - 7)}^{\frac{2}{5}} + 11907 {(x - 7)}^{\frac{1}{5}} + 63^{3}) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.30.6

Eleve $63$ à potência de $3$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 ({(x - 7)}^{\frac{3}{5}} + 189 {(x - 7)}^{\frac{2}{5}} + 11907 {(x - 7)}^{\frac{1}{5}} + 250047) - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.31

Aplique a propriedade distributiva.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 39690 (189 {(x - 7)}^{\frac{2}{5}}) + 39690 (11907 {(x - 7)}^{\frac{1}{5}}) + 39690 \cdot 250047 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.32

Simplifique.

Toque para ver mais passagens...

Etapa 5.2.3.32.1

Multiplique $189$ por $39690$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 39690 (11907 {(x - 7)}^{\frac{1}{5}}) + 39690 \cdot 250047 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.32.2

Multiplique $11907$ por $39690$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 39690 \cdot 250047 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.32.3

Multiplique $39690$ por $250047$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.33

Para escrever $9$ como fração com um denominador comum, multiplique por $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9 \cdot \frac{7}{7})}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.34

Combine $9$ e $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}}}{7} + \frac{9 \cdot 7}{7})}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.35

Combine os numeradores em relação ao denominador comum.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}} + 9 \cdot 7}{7})}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.36

Multiplique $9$ por $7$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 {(\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7})}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.37

Aplique a regra do produto a $\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 \frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{2}}{7^{2}} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.38

Eleve $7$ à potência de $2$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 122523030 \frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{2}}{49} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.39

Cancele o fator comum de $49$ .

Toque para ver mais passagens...

Etapa 5.2.3.39.1

Fatore $49$ de $- 122523030$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 + 49 (- 2500470) (\frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{2}}{49}) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.39.2

Cancele o fator comum.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 + 49 \cdot (- 2500470 \frac{{({(x - 7)}^{\frac{1}{5}} + 63)}^{2}}{49}) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.39.3

Reescreva a expressão.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {({(x - 7)}^{\frac{1}{5}} + 63)}^{2} + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.40

Reescreva ${({(x - 7)}^{\frac{1}{5}} + 63)}^{2}$ como $({(x - 7)}^{\frac{1}{5}} + 63) ({(x - 7)}^{\frac{1}{5}} + 63)$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 (({(x - 7)}^{\frac{1}{5}} + 63) ({(x - 7)}^{\frac{1}{5}} + 63)) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.41

Expanda $({(x - 7)}^{\frac{1}{5}} + 63) ({(x - 7)}^{\frac{1}{5}} + 63)$ usando o método FOIL.

Toque para ver mais passagens...

Etapa 5.2.3.41.1

Aplique a propriedade distributiva.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{1}{5}} ({(x - 7)}^{\frac{1}{5}} + 63) + 63 ({(x - 7)}^{\frac{1}{5}} + 63)) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.41.2

Aplique a propriedade distributiva.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{1}{5}} {(x - 7)}^{\frac{1}{5}} + {(x - 7)}^{\frac{1}{5}} \cdot 63 + 63 ({(x - 7)}^{\frac{1}{5}} + 63)) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.41.3

Aplique a propriedade distributiva.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{1}{5}} {(x - 7)}^{\frac{1}{5}} + {(x - 7)}^{\frac{1}{5}} \cdot 63 + 63 {(x - 7)}^{\frac{1}{5}} + 63 \cdot 63) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.42

Simplifique e combine termos semelhantes.

Toque para ver mais passagens...

Etapa 5.2.3.42.1

Simplifique cada termo.

Toque para ver mais passagens...

Etapa 5.2.3.42.1.1

Multiplique ${(x - 7)}^{\frac{1}{5}}$ por ${(x - 7)}^{\frac{1}{5}}$ somando os expoentes.

Toque para ver mais passagens...

Etapa 5.2.3.42.1.1.1

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{1}{5} + \frac{1}{5}} + {(x - 7)}^{\frac{1}{5}} \cdot 63 + 63 {(x - 7)}^{\frac{1}{5}} + 63 \cdot 63) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.42.1.1.2

Combine os numeradores em relação ao denominador comum.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{1 + 1}{5}} + {(x - 7)}^{\frac{1}{5}} \cdot 63 + 63 {(x - 7)}^{\frac{1}{5}} + 63 \cdot 63) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.42.1.1.3

Some $1$ e $1$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{2}{5}} + {(x - 7)}^{\frac{1}{5}} \cdot 63 + 63 {(x - 7)}^{\frac{1}{5}} + 63 \cdot 63) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.42.1.2

Mova $63$ para a esquerda de ${(x - 7)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{2}{5}} + 63 \cdot {(x - 7)}^{\frac{1}{5}} + 63 {(x - 7)}^{\frac{1}{5}} + 63 \cdot 63) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.42.1.3

Multiplique $63$ por $63$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{2}{5}} + 63 {(x - 7)}^{\frac{1}{5}} + 63 {(x - 7)}^{\frac{1}{5}} + 3969) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.42.2

Some $63 {(x - 7)}^{\frac{1}{5}}$ e $63 {(x - 7)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 ({(x - 7)}^{\frac{2}{5}} + 126 {(x - 7)}^{\frac{1}{5}} + 3969) + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.43

Aplique a propriedade distributiva.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 2500470 (126 {(x - 7)}^{\frac{1}{5}}) - 2500470 \cdot 3969 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.44

Simplifique.

Toque para ver mais passagens...

Etapa 5.2.3.44.1

Multiplique $126$ por $- 2500470$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 2500470 \cdot 3969 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.44.2

Multiplique $- 2500470$ por $3969$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) - 992436536$

Etapa 5.2.3.45

Para escrever $9$ como fração com um denominador comum, multiplique por $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9 \cdot \frac{7}{7}) - 992436536$

Etapa 5.2.3.46

Combine $9$ e $\frac{7}{7}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + \frac{9 \cdot 7}{7}) - 992436536$

Etapa 5.2.3.47

Combine os numeradores em relação ao denominador comum.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}} + 9 \cdot 7}{7}) - 992436536$

Etapa 5.2.3.48

Multiplique $9$ por $7$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 551353635 (\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7}) - 992436536$

Etapa 5.2.3.49

Cancele o fator comum de $7$ .

Toque para ver mais passagens...

Etapa 5.2.3.49.1

Fatore $7$ de $551353635$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 7 (78764805) (\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7}) - 992436536$

Etapa 5.2.3.49.2

Cancele o fator comum.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 7 \cdot (78764805 (\frac{{(x - 7)}^{\frac{1}{5}} + 63}{7})) - 992436536$

Etapa 5.2.3.49.3

Reescreva a expressão.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 ({(x - 7)}^{\frac{1}{5}} + 63) - 992436536$

Etapa 5.2.3.50

Aplique a propriedade distributiva.

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 78764805 \cdot 63 - 992436536$

Etapa 5.2.3.51

Multiplique $78764805$ por $63$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Etapa 5.2.4

Simplifique somando os termos.

Toque para ver mais passagens...

Etapa 5.2.4.1

Combine os termos opostos em $x + 315 {(x - 7)}^{\frac{4}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 315 {(x - 7)}^{\frac{4}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$ .

Toque para ver mais passagens...

Etapa 5.2.4.1.1

Subtraia $315 {(x - 7)}^{\frac{4}{5}}$ de $315 {(x - 7)}^{\frac{4}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 + 0 - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Etapa 5.2.4.1.2

Some $x + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536$ e $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 7501410 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 7501410 {(x - 7)}^{\frac{2}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Etapa 5.2.4.1.3

Some $- 7501410 {(x - 7)}^{\frac{2}{5}}$ e $7501410 {(x - 7)}^{\frac{2}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} + 0 - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Etapa 5.2.4.1.4

Some $x + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}}$ e $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 2500470 {(x - 7)}^{\frac{2}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 2500470 {(x - 7)}^{\frac{2}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Etapa 5.2.4.1.5

Subtraia $2500470 {(x - 7)}^{\frac{2}{5}}$ de $2500470 {(x - 7)}^{\frac{2}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 + 0 - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Etapa 5.2.4.1.6

Some $x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430$ e $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 9924365430 - 315059220 {(x - 7)}^{\frac{1}{5}} - 9924365430 + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Etapa 5.2.4.1.7

Subtraia $9924365430$ de $9924365430$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} + 0 - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Etapa 5.2.4.1.8

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} - 4962182715 + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 4962182715 - 992436536$

Etapa 5.2.4.1.9

Some $- 4962182715$ e $4962182715$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 0 - 992436536$

Etapa 5.2.4.1.10

Some $x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$ e $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 992436536 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} - 992436536$

Etapa 5.2.4.1.11

Subtraia $992436536$ de $992436536$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} + 0 - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Etapa 5.2.4.1.12

Some $x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$ e $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 39690 {(x - 7)}^{\frac{3}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}} - 79380 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Etapa 5.2.4.2

Subtraia $79380 {(x - 7)}^{\frac{3}{5}}$ de $39690 {(x - 7)}^{\frac{3}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 78764805 {(x - 7)}^{\frac{1}{5}} - 39690 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Etapa 5.2.4.3

Combine os termos opostos em $x + 78764805 {(x - 7)}^{\frac{1}{5}} - 39690 {(x - 7)}^{\frac{3}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 39690 {(x - 7)}^{\frac{3}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$ .

Toque para ver mais passagens...

Etapa 5.2.4.3.1

Some $- 39690 {(x - 7)}^{\frac{3}{5}}$ e $39690 {(x - 7)}^{\frac{3}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 78764805 {(x - 7)}^{\frac{1}{5}} + 0 - 315059220 {(x - 7)}^{\frac{1}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Etapa 5.2.4.3.2

Some $x + 78764805 {(x - 7)}^{\frac{1}{5}}$ e $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 78764805 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Etapa 5.2.4.4

Subtraia $315059220 {(x - 7)}^{\frac{1}{5}}$ de $78764805 {(x - 7)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 236294415 {(x - 7)}^{\frac{1}{5}} + 472588830 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Etapa 5.2.4.5

Some $- 236294415 {(x - 7)}^{\frac{1}{5}}$ e $472588830 {(x - 7)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 236294415 {(x - 7)}^{\frac{1}{5}} - 315059220 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Etapa 5.2.4.6

Subtraia $315059220 {(x - 7)}^{\frac{1}{5}}$ de $236294415 {(x - 7)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x - 78764805 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$

Etapa 5.2.4.7

Combine os termos opostos em $x - 78764805 {(x - 7)}^{\frac{1}{5}} + 78764805 {(x - 7)}^{\frac{1}{5}}$ .

Toque para ver mais passagens...

Etapa 5.2.4.7.1

Some $- 78764805 {(x - 7)}^{\frac{1}{5}}$ e $78764805 {(x - 7)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x + 0$

Etapa 5.2.4.7.2

Some $x$ e $0$ .

$f^{- 1} (\frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9) = x$

Etapa 5.3

Avalie $f (f^{- 1} (x))$ .

Toque para ver mais passagens...

Etapa 5.3.1

Estabeleça a função do resultado composto.

$f (f^{- 1} (x))$

Etapa 5.3.2

Avalie $f (16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536)$ substituindo o valor de $f^{- 1}$ em $f$ .

$f (16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536) = \frac{{((16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536) - 7)}^{\frac{1}{5}}}{7} + 9$

Etapa 5.3.3

Subtraia $7$ de $- 992436536$ .

$f (16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536) = \frac{{(16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436543)}^{\frac{1}{5}}}{7} + 9$

Etapa 5.3.4

Para escrever $9$ como fração com um denominador comum, multiplique por $\frac{7}{7}$ .

Etapa 5.3.5

Combine $9$ e $\frac{7}{7}$ .

Etapa 5.3.6

Combine os numeradores em relação ao denominador comum.

Etapa 5.3.7

Multiplique $9$ por $7$ .

Etapa 5.4

Como $f^{- 1} (f (x)) = x$ e $f (f^{- 1} (x)) = x$ , então, $f^{- 1} (x) = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536$ é o inverso de $f (x) = \frac{{(x - 7)}^{\frac{1}{5}}}{7} + 9$ .

$f^{- 1} (x) = 16807 x^{5} - 756315 x^{4} + 13613670 x^{3} - 122523030 x^{2} + 551353635 x - 992436536$