Álgebra Ejemplos

$f (x) = \frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$

Paso 1

Escribe $f (x) = \frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$ como una ecuación.

$y = \frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$

Paso 2

Intercambia las variables.

$x = \frac{{(y - 9)}^{\frac{1}{5}} + 5}{4}$

Paso 3

Resuelve $y$

Toca para ver más pasos...

Paso 3.1

Reescribe la ecuación como $\frac{{(y - 9)}^{\frac{1}{5}} + 5}{4} = x$ .

$\frac{{(y - 9)}^{\frac{1}{5}} + 5}{4} = x$

Paso 3.2

Multiplica ambos lados de la ecuación por $4$ .

$4 \frac{{(y - 9)}^{\frac{1}{5}} + 5}{4} = 4 x$

Paso 3.3

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.3.1

Cancela el factor común de $4$ .

Toca para ver más pasos...

Paso 3.3.1.1

Cancela el factor común.

$4 \frac{{(y - 9)}^{\frac{1}{5}} + 5}{4} = 4 x$

Paso 3.3.1.2

Reescribe la expresión.

${(y - 9)}^{\frac{1}{5}} + 5 = 4 x$

Paso 3.4

Resta $5$ de ambos lados de la ecuación.

${(y - 9)}^{\frac{1}{5}} = 4 x - 5$

Paso 3.5

Eleva cada lado de la ecuación a la potencia de $5$ para eliminar el exponente fraccionario en el lado izquierdo.

${({(y - 9)}^{\frac{1}{5}})}^{5} = {(4 x - 5)}^{5}$

Paso 3.6

Simplifica el exponente.

Toca para ver más pasos...

Paso 3.6.1

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.6.1.1

Simplifica ${({(y - 9)}^{\frac{1}{5}})}^{5}$ .

Toca para ver más pasos...

Paso 3.6.1.1.1

Multiplica los exponentes en ${({(y - 9)}^{\frac{1}{5}})}^{5}$ .

Toca para ver más pasos...

Paso 3.6.1.1.1.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

${(y - 9)}^{\frac{1}{5} \cdot 5} = {(4 x - 5)}^{5}$

Paso 3.6.1.1.1.2

Cancela el factor común de $5$ .

Toca para ver más pasos...

Paso 3.6.1.1.1.2.1

Cancela el factor común.

${(y - 9)}^{\frac{1}{5} \cdot 5} = {(4 x - 5)}^{5}$

Paso 3.6.1.1.1.2.2

Reescribe la expresión.

${(y - 9)}^{1} = {(4 x - 5)}^{5}$

Paso 3.6.1.1.2

Simplifica.

$y - 9 = {(4 x - 5)}^{5}$

Paso 3.6.2

Simplifica el lado derecho.

Toca para ver más pasos...

Paso 3.6.2.1

Simplifica ${(4 x - 5)}^{5}$ .

Toca para ver más pasos...

Paso 3.6.2.1.1

Usa el teorema del binomio.

$y - 9 = {(4 x)}^{5} + 5 {(4 x)}^{4} \cdot - 5 + 10 {(4 x)}^{3} {(- 5)}^{2} + 10 {(4 x)}^{2} {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2

Simplifica cada término.

Toca para ver más pasos...

Paso 3.6.2.1.2.1

Aplica la regla del producto a $4 x$ .

$y - 9 = 4^{5} x^{5} + 5 {(4 x)}^{4} \cdot - 5 + 10 {(4 x)}^{3} {(- 5)}^{2} + 10 {(4 x)}^{2} {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.2

Eleva $4$ a la potencia de $5$ .

$y - 9 = 1024 x^{5} + 5 {(4 x)}^{4} \cdot - 5 + 10 {(4 x)}^{3} {(- 5)}^{2} + 10 {(4 x)}^{2} {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.3

Aplica la regla del producto a $4 x$ .

$y - 9 = 1024 x^{5} + 5 (4^{4} x^{4}) \cdot - 5 + 10 {(4 x)}^{3} {(- 5)}^{2} + 10 {(4 x)}^{2} {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.4

Eleva $4$ a la potencia de $4$ .

$y - 9 = 1024 x^{5} + 5 (256 x^{4}) \cdot - 5 + 10 {(4 x)}^{3} {(- 5)}^{2} + 10 {(4 x)}^{2} {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.5

Multiplica $256$ por $5$ .

$y - 9 = 1024 x^{5} + 1280 x^{4} \cdot - 5 + 10 {(4 x)}^{3} {(- 5)}^{2} + 10 {(4 x)}^{2} {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.6

Multiplica $- 5$ por $1280$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 10 {(4 x)}^{3} {(- 5)}^{2} + 10 {(4 x)}^{2} {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.7

Aplica la regla del producto a $4 x$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 10 (4^{3} x^{3}) {(- 5)}^{2} + 10 {(4 x)}^{2} {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.8

Eleva $4$ a la potencia de $3$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 10 (64 x^{3}) {(- 5)}^{2} + 10 {(4 x)}^{2} {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.9

Multiplica $64$ por $10$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 640 x^{3} {(- 5)}^{2} + 10 {(4 x)}^{2} {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.10

Eleva $- 5$ a la potencia de $2$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 640 x^{3} \cdot 25 + 10 {(4 x)}^{2} {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.11

Multiplica $25$ por $640$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} + 10 {(4 x)}^{2} {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.12

Aplica la regla del producto a $4 x$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} + 10 (4^{2} x^{2}) {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.13

Eleva $4$ a la potencia de $2$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} + 10 (16 x^{2}) {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.14

Multiplica $16$ por $10$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} + 160 x^{2} {(- 5)}^{3} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.15

Eleva $- 5$ a la potencia de $3$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} + 160 x^{2} \cdot - 125 + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.16

Multiplica $- 125$ por $160$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 5 (4 x) {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.17

Multiplica $4$ por $5$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 20 x {(- 5)}^{4} + {(- 5)}^{5}$

Paso 3.6.2.1.2.18

Eleva $- 5$ a la potencia de $4$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 20 x \cdot 625 + {(- 5)}^{5}$

Paso 3.6.2.1.2.19

Multiplica $625$ por $20$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x + {(- 5)}^{5}$

Paso 3.6.2.1.2.20

Eleva $- 5$ a la potencia de $5$ .

$y - 9 = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3125$

Paso 3.7

Mueve todos los términos que no contengan $y$ al lado derecho de la ecuación.

Toca para ver más pasos...

Paso 3.7.1

Suma $9$ a ambos lados de la ecuación.

$y = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3125 + 9$

Paso 3.7.2

Suma $- 3125$ y $9$ .

$y = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3116$

Paso 4

Reemplaza $y$ con $f^{- 1} (x)$ para ver la respuesta final.

$f^{- 1} (x) = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3116$

Paso 5

Verifica si $f^{- 1} (x) = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3116$ es la inversa de $f (x) = \frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$ .

Toca para ver más pasos...

Paso 5.1

Para verificar la inversa, comprueba si $f^{- 1} (f (x)) = x$ y $f (f^{- 1} (x)) = x$ .

Paso 5.2

Evalúa $f^{- 1} (f (x))$ .

Toca para ver más pasos...

Paso 5.2.1

Establece la función de resultado compuesta.

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

Paso 5.2.2

Evalúa $f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})$ mediante la sustitución del valor de $f$ en $f^{- 1}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = 1024 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3

Simplifica cada término.

Toca para ver más pasos...

Paso 5.2.3.1

Aplica la regla del producto a $\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = 1024 (\frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{5}}{4^{5}}) - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.2

Eleva $4$ a la potencia de $5$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = 1024 (\frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{5}}{1024}) - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.3

Cancela el factor común de $1024$ .

Toca para ver más pasos...

Paso 5.2.3.3.1

Cancela el factor común.

Paso 5.2.3.3.2

Reescribe la expresión.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = {({(x - 9)}^{\frac{1}{5}} + 5)}^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.4

Usa el teorema del binomio.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = {({(x - 9)}^{\frac{1}{5}})}^{5} + 5 {({(x - 9)}^{\frac{1}{5}})}^{4} \cdot 5 + 10 {({(x - 9)}^{\frac{1}{5}})}^{3} \cdot 5^{2} + 10 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{3} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5

Simplifica cada término.

Toca para ver más pasos...

Paso 5.2.3.5.1

Multiplica los exponentes en ${({(x - 9)}^{\frac{1}{5}})}^{5}$ .

Toca para ver más pasos...

Paso 5.2.3.5.1.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = {(x - 9)}^{\frac{1}{5} \cdot 5} + 5 {({(x - 9)}^{\frac{1}{5}})}^{4} \cdot 5 + 10 {({(x - 9)}^{\frac{1}{5}})}^{3} \cdot 5^{2} + 10 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{3} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.1.2

Cancela el factor común de $5$ .

Toca para ver más pasos...

Paso 5.2.3.5.1.2.1

Cancela el factor común.

Paso 5.2.3.5.1.2.2

Reescribe la expresión.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = (x - 9) + 5 {({(x - 9)}^{\frac{1}{5}})}^{4} \cdot 5 + 10 {({(x - 9)}^{\frac{1}{5}})}^{3} \cdot 5^{2} + 10 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{3} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.2

Simplifica.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 5 {({(x - 9)}^{\frac{1}{5}})}^{4} \cdot 5 + 10 {({(x - 9)}^{\frac{1}{5}})}^{3} \cdot 5^{2} + 10 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{3} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.3

Multiplica los exponentes en ${({(x - 9)}^{\frac{1}{5}})}^{4}$ .

Toca para ver más pasos...

Paso 5.2.3.5.3.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 5 {(x - 9)}^{\frac{1}{5} \cdot 4} \cdot 5 + 10 {({(x - 9)}^{\frac{1}{5}})}^{3} \cdot 5^{2} + 10 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{3} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.3.2

Combina $\frac{1}{5}$ y $4$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 5 {(x - 9)}^{\frac{4}{5}} \cdot 5 + 10 {({(x - 9)}^{\frac{1}{5}})}^{3} \cdot 5^{2} + 10 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{3} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.4

Multiplica $5$ por $5$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 10 {({(x - 9)}^{\frac{1}{5}})}^{3} \cdot 5^{2} + 10 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{3} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.5

Multiplica los exponentes en ${({(x - 9)}^{\frac{1}{5}})}^{3}$ .

Toca para ver más pasos...

Paso 5.2.3.5.5.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 10 {(x - 9)}^{\frac{1}{5} \cdot 3} \cdot 5^{2} + 10 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{3} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.5.2

Combina $\frac{1}{5}$ y $3$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 10 {(x - 9)}^{\frac{3}{5}} \cdot 5^{2} + 10 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{3} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.6

Eleva $5$ a la potencia de $2$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 10 {(x - 9)}^{\frac{3}{5}} \cdot 25 + 10 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{3} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.7

Multiplica $25$ por $10$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 10 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{3} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.8

Multiplica los exponentes en ${({(x - 9)}^{\frac{1}{5}})}^{2}$ .

Toca para ver más pasos...

Paso 5.2.3.5.8.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 10 {(x - 9)}^{\frac{1}{5} \cdot 2} \cdot 5^{3} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.8.2

Combina $\frac{1}{5}$ y $2$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 10 {(x - 9)}^{\frac{2}{5}} \cdot 5^{3} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.9

Eleva $5$ a la potencia de $3$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 10 {(x - 9)}^{\frac{2}{5}} \cdot 125 + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.10

Multiplica $125$ por $10$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 5 {(x - 9)}^{\frac{1}{5}} \cdot 5^{4} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.11

Multiplica $5$ por $5^{4}$ sumando los exponentes.

Toca para ver más pasos...

Paso 5.2.3.5.11.1

Mueve $5^{4}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 5^{4} \cdot (5 {(x - 9)}^{\frac{1}{5}}) + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.11.2

Multiplica $5^{4}$ por $5$ .

Toca para ver más pasos...

Paso 5.2.3.5.11.2.1

Eleva $5$ a la potencia de $1$ .

Paso 5.2.3.5.11.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 5^{4 + 1} {(x - 9)}^{\frac{1}{5}} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.11.3

Suma $4$ y $1$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 5^{5} {(x - 9)}^{\frac{1}{5}} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.12

Eleva $5$ a la potencia de $5$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 5^{5} - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.5.13

Eleva $5$ a la potencia de $5$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9 + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3125 - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.6

Suma $- 9$ y $3125$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 6400 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.7

Aplica la regla del producto a $\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 6400 \frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{4}}{4^{4}} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.8

Eleva $4$ a la potencia de $4$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 6400 \frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{4}}{256} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.9

Cancela el factor común de $256$ .

Toca para ver más pasos...

Paso 5.2.3.9.1

Factoriza $256$ de $- 6400$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 + 256 (- 25) (\frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{4}}{256}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.9.2

Cancela el factor común.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 + 256 \cdot (- 25 \frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{4}}{256}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.9.3

Reescribe la expresión.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {({(x - 9)}^{\frac{1}{5}} + 5)}^{4} + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.10

Usa el teorema del binomio.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 ({({(x - 9)}^{\frac{1}{5}})}^{4} + 4 {({(x - 9)}^{\frac{1}{5}})}^{3} \cdot 5 + 6 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{2} + 4 {(x - 9)}^{\frac{1}{5}} \cdot 5^{3} + 5^{4}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.11

Simplifica cada término.

Toca para ver más pasos...

Paso 5.2.3.11.1

Multiplica los exponentes en ${({(x - 9)}^{\frac{1}{5}})}^{4}$ .

Toca para ver más pasos...

Paso 5.2.3.11.1.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 ({(x - 9)}^{\frac{1}{5} \cdot 4} + 4 {({(x - 9)}^{\frac{1}{5}})}^{3} \cdot 5 + 6 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{2} + 4 {(x - 9)}^{\frac{1}{5}} \cdot 5^{3} + 5^{4}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.11.1.2

Combina $\frac{1}{5}$ y $4$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 ({(x - 9)}^{\frac{4}{5}} + 4 {({(x - 9)}^{\frac{1}{5}})}^{3} \cdot 5 + 6 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{2} + 4 {(x - 9)}^{\frac{1}{5}} \cdot 5^{3} + 5^{4}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.11.2

Multiplica los exponentes en ${({(x - 9)}^{\frac{1}{5}})}^{3}$ .

Toca para ver más pasos...

Paso 5.2.3.11.2.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 ({(x - 9)}^{\frac{4}{5}} + 4 {(x - 9)}^{\frac{1}{5} \cdot 3} \cdot 5 + 6 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{2} + 4 {(x - 9)}^{\frac{1}{5}} \cdot 5^{3} + 5^{4}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.11.2.2

Combina $\frac{1}{5}$ y $3$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 ({(x - 9)}^{\frac{4}{5}} + 4 {(x - 9)}^{\frac{3}{5}} \cdot 5 + 6 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{2} + 4 {(x - 9)}^{\frac{1}{5}} \cdot 5^{3} + 5^{4}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.11.3

Multiplica $5$ por $4$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 ({(x - 9)}^{\frac{4}{5}} + 20 {(x - 9)}^{\frac{3}{5}} + 6 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5^{2} + 4 {(x - 9)}^{\frac{1}{5}} \cdot 5^{3} + 5^{4}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.11.4

Multiplica los exponentes en ${({(x - 9)}^{\frac{1}{5}})}^{2}$ .

Toca para ver más pasos...

Paso 5.2.3.11.4.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 ({(x - 9)}^{\frac{4}{5}} + 20 {(x - 9)}^{\frac{3}{5}} + 6 {(x - 9)}^{\frac{1}{5} \cdot 2} \cdot 5^{2} + 4 {(x - 9)}^{\frac{1}{5}} \cdot 5^{3} + 5^{4}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.11.4.2

Combina $\frac{1}{5}$ y $2$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 ({(x - 9)}^{\frac{4}{5}} + 20 {(x - 9)}^{\frac{3}{5}} + 6 {(x - 9)}^{\frac{2}{5}} \cdot 5^{2} + 4 {(x - 9)}^{\frac{1}{5}} \cdot 5^{3} + 5^{4}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.11.5

Eleva $5$ a la potencia de $2$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 ({(x - 9)}^{\frac{4}{5}} + 20 {(x - 9)}^{\frac{3}{5}} + 6 {(x - 9)}^{\frac{2}{5}} \cdot 25 + 4 {(x - 9)}^{\frac{1}{5}} \cdot 5^{3} + 5^{4}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.11.6

Multiplica $25$ por $6$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 ({(x - 9)}^{\frac{4}{5}} + 20 {(x - 9)}^{\frac{3}{5}} + 150 {(x - 9)}^{\frac{2}{5}} + 4 {(x - 9)}^{\frac{1}{5}} \cdot 5^{3} + 5^{4}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.11.7

Eleva $5$ a la potencia de $3$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 ({(x - 9)}^{\frac{4}{5}} + 20 {(x - 9)}^{\frac{3}{5}} + 150 {(x - 9)}^{\frac{2}{5}} + 4 {(x - 9)}^{\frac{1}{5}} \cdot 125 + 5^{4}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.11.8

Multiplica $125$ por $4$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 ({(x - 9)}^{\frac{4}{5}} + 20 {(x - 9)}^{\frac{3}{5}} + 150 {(x - 9)}^{\frac{2}{5}} + 500 {(x - 9)}^{\frac{1}{5}} + 5^{4}) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.11.9

Eleva $5$ a la potencia de $4$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 ({(x - 9)}^{\frac{4}{5}} + 20 {(x - 9)}^{\frac{3}{5}} + 150 {(x - 9)}^{\frac{2}{5}} + 500 {(x - 9)}^{\frac{1}{5}} + 625) + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.12

Aplica la propiedad distributiva.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 25 (20 {(x - 9)}^{\frac{3}{5}}) - 25 (150 {(x - 9)}^{\frac{2}{5}}) - 25 (500 {(x - 9)}^{\frac{1}{5}}) - 25 \cdot 625 + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.13

Simplifica.

Toca para ver más pasos...

Paso 5.2.3.13.1

Multiplica $20$ por $- 25$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 25 (150 {(x - 9)}^{\frac{2}{5}}) - 25 (500 {(x - 9)}^{\frac{1}{5}}) - 25 \cdot 625 + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.13.2

Multiplica $150$ por $- 25$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 25 (500 {(x - 9)}^{\frac{1}{5}}) - 25 \cdot 625 + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.13.3

Multiplica $500$ por $- 25$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 25 \cdot 625 + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.13.4

Multiplica $- 25$ por $625$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 16000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.14

Aplica la regla del producto a $\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 16000 (\frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{3}}{4^{3}}) - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.15

Eleva $4$ a la potencia de $3$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 16000 (\frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{3}}{64}) - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.16

Cancela el factor común de $64$ .

Toca para ver más pasos...

Paso 5.2.3.16.1

Factoriza $64$ de $16000$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 64 (250) (\frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{3}}{64}) - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.16.2

Cancela el factor común.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 64 \cdot (250 (\frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{3}}{64})) - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.16.3

Reescribe la expresión.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {({(x - 9)}^{\frac{1}{5}} + 5)}^{3} - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.17

Usa el teorema del binomio.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 ({({(x - 9)}^{\frac{1}{5}})}^{3} + 3 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5 + 3 {(x - 9)}^{\frac{1}{5}} \cdot 5^{2} + 5^{3}) - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.18

Simplifica cada término.

Toca para ver más pasos...

Paso 5.2.3.18.1

Multiplica los exponentes en ${({(x - 9)}^{\frac{1}{5}})}^{3}$ .

Toca para ver más pasos...

Paso 5.2.3.18.1.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 ({(x - 9)}^{\frac{1}{5} \cdot 3} + 3 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5 + 3 {(x - 9)}^{\frac{1}{5}} \cdot 5^{2} + 5^{3}) - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.18.1.2

Combina $\frac{1}{5}$ y $3$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 ({(x - 9)}^{\frac{3}{5}} + 3 {({(x - 9)}^{\frac{1}{5}})}^{2} \cdot 5 + 3 {(x - 9)}^{\frac{1}{5}} \cdot 5^{2} + 5^{3}) - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.18.2

Multiplica los exponentes en ${({(x - 9)}^{\frac{1}{5}})}^{2}$ .

Toca para ver más pasos...

Paso 5.2.3.18.2.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 ({(x - 9)}^{\frac{3}{5}} + 3 {(x - 9)}^{\frac{1}{5} \cdot 2} \cdot 5 + 3 {(x - 9)}^{\frac{1}{5}} \cdot 5^{2} + 5^{3}) - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.18.2.2

Combina $\frac{1}{5}$ y $2$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 ({(x - 9)}^{\frac{3}{5}} + 3 {(x - 9)}^{\frac{2}{5}} \cdot 5 + 3 {(x - 9)}^{\frac{1}{5}} \cdot 5^{2} + 5^{3}) - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.18.3

Multiplica $5$ por $3$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 ({(x - 9)}^{\frac{3}{5}} + 15 {(x - 9)}^{\frac{2}{5}} + 3 {(x - 9)}^{\frac{1}{5}} \cdot 5^{2} + 5^{3}) - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.18.4

Eleva $5$ a la potencia de $2$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 ({(x - 9)}^{\frac{3}{5}} + 15 {(x - 9)}^{\frac{2}{5}} + 3 {(x - 9)}^{\frac{1}{5}} \cdot 25 + 5^{3}) - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.18.5

Multiplica $25$ por $3$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 ({(x - 9)}^{\frac{3}{5}} + 15 {(x - 9)}^{\frac{2}{5}} + 75 {(x - 9)}^{\frac{1}{5}} + 5^{3}) - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.18.6

Eleva $5$ a la potencia de $3$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 ({(x - 9)}^{\frac{3}{5}} + 15 {(x - 9)}^{\frac{2}{5}} + 75 {(x - 9)}^{\frac{1}{5}} + 125) - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.19

Aplica la propiedad distributiva.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 250 (15 {(x - 9)}^{\frac{2}{5}}) + 250 (75 {(x - 9)}^{\frac{1}{5}}) + 250 \cdot 125 - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.20

Simplifica.

Toca para ver más pasos...

Paso 5.2.3.20.1

Multiplica $15$ por $250$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 250 (75 {(x - 9)}^{\frac{1}{5}}) + 250 \cdot 125 - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.20.2

Multiplica $75$ por $250$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 250 \cdot 125 - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.20.3

Multiplica $250$ por $125$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 20000 {(\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.21

Aplica la regla del producto a $\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 20000 \frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{2}}{4^{2}} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.22

Eleva $4$ a la potencia de $2$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 20000 \frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{2}}{16} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.23

Cancela el factor común de $16$ .

Toca para ver más pasos...

Paso 5.2.3.23.1

Factoriza $16$ de $- 20000$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 + 16 (- 1250) (\frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{2}}{16}) + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.23.2

Cancela el factor común.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 + 16 \cdot (- 1250 \frac{{({(x - 9)}^{\frac{1}{5}} + 5)}^{2}}{16}) + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.23.3

Reescribe la expresión.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {({(x - 9)}^{\frac{1}{5}} + 5)}^{2} + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.24

Reescribe ${({(x - 9)}^{\frac{1}{5}} + 5)}^{2}$ como $({(x - 9)}^{\frac{1}{5}} + 5) ({(x - 9)}^{\frac{1}{5}} + 5)$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 (({(x - 9)}^{\frac{1}{5}} + 5) ({(x - 9)}^{\frac{1}{5}} + 5)) + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.25

Expande $({(x - 9)}^{\frac{1}{5}} + 5) ({(x - 9)}^{\frac{1}{5}} + 5)$ con el método PEIU (primero, exterior, interior, ultimo).

Toca para ver más pasos...

Paso 5.2.3.25.1

Aplica la propiedad distributiva.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 ({(x - 9)}^{\frac{1}{5}} ({(x - 9)}^{\frac{1}{5}} + 5) + 5 ({(x - 9)}^{\frac{1}{5}} + 5)) + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.25.2

Aplica la propiedad distributiva.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 ({(x - 9)}^{\frac{1}{5}} {(x - 9)}^{\frac{1}{5}} + {(x - 9)}^{\frac{1}{5}} \cdot 5 + 5 ({(x - 9)}^{\frac{1}{5}} + 5)) + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.25.3

Aplica la propiedad distributiva.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 ({(x - 9)}^{\frac{1}{5}} {(x - 9)}^{\frac{1}{5}} + {(x - 9)}^{\frac{1}{5}} \cdot 5 + 5 {(x - 9)}^{\frac{1}{5}} + 5 \cdot 5) + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.26

Simplifica y combina los términos similares.

Toca para ver más pasos...

Paso 5.2.3.26.1

Simplifica cada término.

Toca para ver más pasos...

Paso 5.2.3.26.1.1

Multiplica ${(x - 9)}^{\frac{1}{5}}$ por ${(x - 9)}^{\frac{1}{5}}$ sumando los exponentes.

Toca para ver más pasos...

Paso 5.2.3.26.1.1.1

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 ({(x - 9)}^{\frac{1}{5} + \frac{1}{5}} + {(x - 9)}^{\frac{1}{5}} \cdot 5 + 5 {(x - 9)}^{\frac{1}{5}} + 5 \cdot 5) + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.26.1.1.2

Combina los numeradores sobre el denominador común.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 ({(x - 9)}^{\frac{1 + 1}{5}} + {(x - 9)}^{\frac{1}{5}} \cdot 5 + 5 {(x - 9)}^{\frac{1}{5}} + 5 \cdot 5) + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.26.1.1.3

Suma $1$ y $1$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 ({(x - 9)}^{\frac{2}{5}} + {(x - 9)}^{\frac{1}{5}} \cdot 5 + 5 {(x - 9)}^{\frac{1}{5}} + 5 \cdot 5) + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.26.1.2

Mueve $5$ a la izquierda de ${(x - 9)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 ({(x - 9)}^{\frac{2}{5}} + 5 \cdot {(x - 9)}^{\frac{1}{5}} + 5 {(x - 9)}^{\frac{1}{5}} + 5 \cdot 5) + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.26.1.3

Multiplica $5$ por $5$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 ({(x - 9)}^{\frac{2}{5}} + 5 {(x - 9)}^{\frac{1}{5}} + 5 {(x - 9)}^{\frac{1}{5}} + 25) + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.26.2

Suma $5 {(x - 9)}^{\frac{1}{5}}$ y $5 {(x - 9)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 ({(x - 9)}^{\frac{2}{5}} + 10 {(x - 9)}^{\frac{1}{5}} + 25) + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.27

Aplica la propiedad distributiva.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 1250 (10 {(x - 9)}^{\frac{1}{5}}) - 1250 \cdot 25 + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.28

Simplifica.

Toca para ver más pasos...

Paso 5.2.3.28.1

Multiplica $10$ por $- 1250$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 1250 \cdot 25 + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.28.2

Multiplica $- 1250$ por $25$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 12500 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.29

Cancela el factor común de $4$ .

Toca para ver más pasos...

Paso 5.2.3.29.1

Factoriza $4$ de $12500$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 4 (3125) (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) - 3116$

Paso 5.2.3.29.2

Cancela el factor común.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 4 \cdot (3125 (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})) - 3116$

Paso 5.2.3.29.3

Reescribe la expresión.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 3125 ({(x - 9)}^{\frac{1}{5}} + 5) - 3116$

Paso 5.2.3.30

Aplica la propiedad distributiva.

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 3125 {(x - 9)}^{\frac{1}{5}} + 3125 \cdot 5 - 3116$

Paso 5.2.3.31

Multiplica $3125$ por $5$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 3125 {(x - 9)}^{\frac{1}{5}} + 15625 - 3116$

Paso 5.2.4

Simplifica mediante la adición de términos.

Toca para ver más pasos...

Paso 5.2.4.1

Combina los términos opuestos en $x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 3125 {(x - 9)}^{\frac{1}{5}} + 15625 - 3116$ .

Toca para ver más pasos...

Paso 5.2.4.1.1

Resta $25 {(x - 9)}^{\frac{4}{5}}$ de $25 {(x - 9)}^{\frac{4}{5}}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 + 0 - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 3125 {(x - 9)}^{\frac{1}{5}} + 15625 - 3116$

Paso 5.2.4.1.2

Suma $x + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116$ y $0$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 3125 {(x - 9)}^{\frac{1}{5}} + 15625 - 3116$

Paso 5.2.4.1.3

Suma $- 3750 {(x - 9)}^{\frac{2}{5}}$ y $3750 {(x - 9)}^{\frac{2}{5}}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 500 {(x - 9)}^{\frac{3}{5}} + 0 - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 3125 {(x - 9)}^{\frac{1}{5}} + 15625 - 3116$

Paso 5.2.4.1.4

Suma $x + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 500 {(x - 9)}^{\frac{3}{5}}$ y $0$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 500 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 3125 {(x - 9)}^{\frac{1}{5}} + 15625 - 3116$

Paso 5.2.4.1.5

Resta $1250 {(x - 9)}^{\frac{2}{5}}$ de $1250 {(x - 9)}^{\frac{2}{5}}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 250 {(x - 9)}^{\frac{3}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 500 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 + 0 - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 3125 {(x - 9)}^{\frac{1}{5}} + 15625 - 3116$

Paso 5.2.4.1.6

Suma $x + 250 {(x - 9)}^{\frac{3}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 500 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250$ y $0$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 250 {(x - 9)}^{\frac{3}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 500 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 3125 {(x - 9)}^{\frac{1}{5}} + 15625 - 3116$

Paso 5.2.4.1.7

Resta $31250$ de $31250$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 250 {(x - 9)}^{\frac{3}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 500 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 0 - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 15625 - 3116$

Paso 5.2.4.1.8

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 250 {(x - 9)}^{\frac{3}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 500 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 15625 - 3116$

Paso 5.2.4.1.9

Suma $- 15625$ y $15625$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 250 {(x - 9)}^{\frac{3}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 500 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 0 - 3116$

Paso 5.2.4.1.10

Suma $x + 250 {(x - 9)}^{\frac{3}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 500 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$ y $0$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 250 {(x - 9)}^{\frac{3}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 500 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} - 3116$

Paso 5.2.4.1.11

Resta $3116$ de $3116$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 250 {(x - 9)}^{\frac{3}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 0 - 500 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$

Paso 5.2.4.1.12

Suma $x + 250 {(x - 9)}^{\frac{3}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$ y $0$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 250 {(x - 9)}^{\frac{3}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$

Paso 5.2.4.2

Resta $500 {(x - 9)}^{\frac{3}{5}}$ de $250 {(x - 9)}^{\frac{3}{5}}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 3125 {(x - 9)}^{\frac{1}{5}} - 250 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$

Paso 5.2.4.3

Combina los términos opuestos en $x + 3125 {(x - 9)}^{\frac{1}{5}} - 250 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$ .

Toca para ver más pasos...

Paso 5.2.4.3.1

Suma $- 250 {(x - 9)}^{\frac{3}{5}}$ y $250 {(x - 9)}^{\frac{3}{5}}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 3125 {(x - 9)}^{\frac{1}{5}} + 0 - 12500 {(x - 9)}^{\frac{1}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$

Paso 5.2.4.3.2

Suma $x + 3125 {(x - 9)}^{\frac{1}{5}}$ y $0$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 3125 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$

Paso 5.2.4.4

Resta $12500 {(x - 9)}^{\frac{1}{5}}$ de $3125 {(x - 9)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 9375 {(x - 9)}^{\frac{1}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$

Paso 5.2.4.5

Suma $- 9375 {(x - 9)}^{\frac{1}{5}}$ y $18750 {(x - 9)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 9375 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$

Paso 5.2.4.6

Resta $12500 {(x - 9)}^{\frac{1}{5}}$ de $9375 {(x - 9)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x - 3125 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$

Paso 5.2.4.7

Combina los términos opuestos en $x - 3125 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$ .

Toca para ver más pasos...

Paso 5.2.4.7.1

Suma $- 3125 {(x - 9)}^{\frac{1}{5}}$ y $3125 {(x - 9)}^{\frac{1}{5}}$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x + 0$

Paso 5.2.4.7.2

Suma $x$ y $0$ .

$f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}) = x$

Paso 5.3

Evalúa $f (f^{- 1} (x))$ .

Toca para ver más pasos...

Paso 5.3.1

Establece la función de resultado compuesta.

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

Paso 5.3.2

Evalúa $f (1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3116)$ mediante la sustitución del valor de $f^{- 1}$ en $f$ .

$f (1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3116) = \frac{{((1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3116) - 9)}^{\frac{1}{5}} + 5}{4}$

Paso 5.3.3

Resta $9$ de $- 3116$ .

$f (1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3116) = \frac{{(1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3125)}^{\frac{1}{5}} + 5}{4}$

Paso 5.4

Como $f^{- 1} (f (x)) = x$ y $f (f^{- 1} (x)) = x$ , entonces $f^{- 1} (x) = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3116$ es la inversa de $f (x) = \frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$ .

$f^{- 1} (x) = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3116$