Algebra Beispiele

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

Schritt 1

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

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

Schritt 2

Vertausche die Variablen.

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

Schritt 3

Löse nach $y$ auf.

Tippen, um mehr Schritte zu sehen ...

Schritt 3.1

Schreibe die Gleichung als $\frac{{(y - 9)}^{\frac{1}{5}} + 5}{4} = x$ um.

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

Schritt 3.2

Multipliziere beide Seiten der Gleichung mit $4$ .

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

Schritt 3.3

Vereinfache die linke Seite.

Tippen, um mehr Schritte zu sehen ...

Schritt 3.3.1

Kürze den gemeinsamen Faktor von $4$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 3.3.1.1

Kürze den gemeinsamen Faktor.

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

Schritt 3.3.1.2

Forme den Ausdruck um.

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

Schritt 3.4

Subtrahiere $5$ von beiden Seiten der Gleichung.

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

Schritt 3.5

Potenziere jede Seite der Gleichung mit $5$ , um den gebrochenen Exponenten auf der linken Seite zu eliminieren.

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

Schritt 3.6

Vereinfache den Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 3.6.1

Vereinfache die linke Seite.

Tippen, um mehr Schritte zu sehen ...

Schritt 3.6.1.1

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

Tippen, um mehr Schritte zu sehen ...

Schritt 3.6.1.1.1

Multipliziere die Exponenten in ${({(y - 9)}^{\frac{1}{5}})}^{5}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 3.6.1.1.1.1

Wende die Potenzregel an und multipliziere die Exponenten, ${(a^{m})}^{n} = a^{m n}$ .

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

Schritt 3.6.1.1.1.2

Kürze den gemeinsamen Faktor von $5$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 3.6.1.1.1.2.1

Kürze den gemeinsamen Faktor.

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

Schritt 3.6.1.1.1.2.2

Forme den Ausdruck um.

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

Schritt 3.6.1.1.2

Vereinfache.

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

Schritt 3.6.2

Vereinfache die rechte Seite.

Tippen, um mehr Schritte zu sehen ...

Schritt 3.6.2.1

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

Tippen, um mehr Schritte zu sehen ...

Schritt 3.6.2.1.1

Wende den binomischen Lehrsatz an.

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

Schritt 3.6.2.1.2

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 3.6.2.1.2.1

Wende die Produktregel auf $4 x$ an.

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

Schritt 3.6.2.1.2.2

Potenziere $4$ mit $5$ .

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

Schritt 3.6.2.1.2.3

Wende die Produktregel auf $4 x$ an.

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

Schritt 3.6.2.1.2.4

Potenziere $4$ mit $4$ .

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

Schritt 3.6.2.1.2.5

Mutltipliziere $256$ mit $5$ .

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

Schritt 3.6.2.1.2.6

Mutltipliziere $- 5$ mit $1280$ .

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

Schritt 3.6.2.1.2.7

Wende die Produktregel auf $4 x$ an.

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

Schritt 3.6.2.1.2.8

Potenziere $4$ mit $3$ .

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

Schritt 3.6.2.1.2.9

Mutltipliziere $64$ mit $10$ .

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

Schritt 3.6.2.1.2.10

Potenziere $- 5$ mit $2$ .

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

Schritt 3.6.2.1.2.11

Mutltipliziere $25$ mit $640$ .

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

Schritt 3.6.2.1.2.12

Wende die Produktregel auf $4 x$ an.

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

Schritt 3.6.2.1.2.13

Potenziere $4$ mit $2$ .

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

Schritt 3.6.2.1.2.14

Mutltipliziere $16$ mit $10$ .

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

Schritt 3.6.2.1.2.15

Potenziere $- 5$ mit $3$ .

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

Schritt 3.6.2.1.2.16

Mutltipliziere $- 125$ mit $160$ .

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

Schritt 3.6.2.1.2.17

Mutltipliziere $4$ mit $5$ .

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

Schritt 3.6.2.1.2.18

Potenziere $- 5$ mit $4$ .

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

Schritt 3.6.2.1.2.19

Mutltipliziere $625$ mit $20$ .

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

Schritt 3.6.2.1.2.20

Potenziere $- 5$ mit $5$ .

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

Schritt 3.7

Bringe alle Terme, die nicht $y$ enthalten, auf die rechte Seite der Gleichung.

Tippen, um mehr Schritte zu sehen ...

Schritt 3.7.1

Addiere $9$ zu beiden Seiten der Gleichung.

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

Schritt 3.7.2

Addiere $- 3125$ und $9$ .

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

Schritt 4

Ersetze $y$ durch $f^{- 1} (x)$ , um die endgültige Lösung anzuzeigen.

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

Schritt 5

Überprüfe, ob $f^{- 1} (x) = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3116$ die Umkehrfunktion von $f (x) = \frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$ ist.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.1

Um die inverse Funktion (Umkehrfunktion) zu prüfen, prüfe ob $f^{- 1} (f (x)) = x$ ist und $f (f^{- 1} (x)) = x$ ist.

Schritt 5.2

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

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.1

Bilde die verkettete Ergebnisfunktion.

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

Schritt 5.2.2

Berechne $f^{- 1} (\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4})$ durch Einsetzen des Wertes von $f$ in $f^{- 1}$ .

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

Schritt 5.2.3

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.1

Wende die Produktregel auf $\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$ an.

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

Schritt 5.2.3.2

Potenziere $4$ mit $5$ .

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

Schritt 5.2.3.3

Kürze den gemeinsamen Faktor von $1024$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.3.1

Kürze den gemeinsamen Faktor.

Schritt 5.2.3.3.2

Forme den Ausdruck um.

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

Schritt 5.2.3.4

Wende den binomischen Lehrsatz an.

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

Schritt 5.2.3.5

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.5.1

Multipliziere die Exponenten in ${({(x - 9)}^{\frac{1}{5}})}^{5}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.5.1.1

Wende die Potenzregel an und multipliziere die Exponenten, ${(a^{m})}^{n} = a^{m n}$ .

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

Schritt 5.2.3.5.1.2

Kürze den gemeinsamen Faktor von $5$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.5.1.2.1

Kürze den gemeinsamen Faktor.

Schritt 5.2.3.5.1.2.2

Forme den Ausdruck um.

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

Schritt 5.2.3.5.2

Vereinfache.

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

Schritt 5.2.3.5.3

Multipliziere die Exponenten in ${({(x - 9)}^{\frac{1}{5}})}^{4}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.5.3.1

Wende die Potenzregel an und multipliziere die Exponenten, ${(a^{m})}^{n} = a^{m n}$ .

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

Schritt 5.2.3.5.3.2

Kombiniere $\frac{1}{5}$ und $4$ .

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

Schritt 5.2.3.5.4

Mutltipliziere $5$ mit $5$ .

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

Schritt 5.2.3.5.5

Multipliziere die Exponenten in ${({(x - 9)}^{\frac{1}{5}})}^{3}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.5.5.1

Wende die Potenzregel an und multipliziere die Exponenten, ${(a^{m})}^{n} = a^{m n}$ .

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

Schritt 5.2.3.5.5.2

Kombiniere $\frac{1}{5}$ und $3$ .

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

Schritt 5.2.3.5.6

Potenziere $5$ mit $2$ .

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

Schritt 5.2.3.5.7

Mutltipliziere $25$ mit $10$ .

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

Schritt 5.2.3.5.8

Multipliziere die Exponenten in ${({(x - 9)}^{\frac{1}{5}})}^{2}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.5.8.1

Wende die Potenzregel an und multipliziere die Exponenten, ${(a^{m})}^{n} = a^{m n}$ .

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

Schritt 5.2.3.5.8.2

Kombiniere $\frac{1}{5}$ und $2$ .

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

Schritt 5.2.3.5.9

Potenziere $5$ mit $3$ .

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

Schritt 5.2.3.5.10

Mutltipliziere $125$ mit $10$ .

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

Schritt 5.2.3.5.11

Multipliziere $5$ mit $5^{4}$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.5.11.1

Bewege $5^{4}$ .

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

Schritt 5.2.3.5.11.2

Mutltipliziere $5^{4}$ mit $5$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.5.11.2.1

Potenziere $5$ mit $1$ .

Schritt 5.2.3.5.11.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 5.2.3.5.11.3

Addiere $4$ und $1$ .

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

Schritt 5.2.3.5.12

Potenziere $5$ mit $5$ .

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

Schritt 5.2.3.5.13

Potenziere $5$ mit $5$ .

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

Schritt 5.2.3.6

Addiere $- 9$ und $3125$ .

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

Schritt 5.2.3.7

Wende die Produktregel auf $\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$ an.

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

Schritt 5.2.3.8

Potenziere $4$ mit $4$ .

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

Schritt 5.2.3.9

Kürze den gemeinsamen Faktor von $256$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.9.1

Faktorisiere $256$ aus $- 6400$ heraus.

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

Schritt 5.2.3.9.2

Kürze den gemeinsamen Faktor.

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

Schritt 5.2.3.9.3

Forme den Ausdruck um.

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

Schritt 5.2.3.10

Wende den binomischen Lehrsatz an.

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

Schritt 5.2.3.11

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.11.1

Multipliziere die Exponenten in ${({(x - 9)}^{\frac{1}{5}})}^{4}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.11.1.1

Wende die Potenzregel an und multipliziere die Exponenten, ${(a^{m})}^{n} = a^{m n}$ .

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

Schritt 5.2.3.11.1.2

Kombiniere $\frac{1}{5}$ und $4$ .

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

Schritt 5.2.3.11.2

Multipliziere die Exponenten in ${({(x - 9)}^{\frac{1}{5}})}^{3}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.11.2.1

Wende die Potenzregel an und multipliziere die Exponenten, ${(a^{m})}^{n} = a^{m n}$ .

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

Schritt 5.2.3.11.2.2

Kombiniere $\frac{1}{5}$ und $3$ .

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

Schritt 5.2.3.11.3

Mutltipliziere $5$ mit $4$ .

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

Schritt 5.2.3.11.4

Multipliziere die Exponenten in ${({(x - 9)}^{\frac{1}{5}})}^{2}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.11.4.1

Wende die Potenzregel an und multipliziere die Exponenten, ${(a^{m})}^{n} = a^{m n}$ .

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

Schritt 5.2.3.11.4.2

Kombiniere $\frac{1}{5}$ und $2$ .

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

Schritt 5.2.3.11.5

Potenziere $5$ mit $2$ .

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

Schritt 5.2.3.11.6

Mutltipliziere $25$ mit $6$ .

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

Schritt 5.2.3.11.7

Potenziere $5$ mit $3$ .

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

Schritt 5.2.3.11.8

Mutltipliziere $125$ mit $4$ .

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

Schritt 5.2.3.11.9

Potenziere $5$ mit $4$ .

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

Schritt 5.2.3.12

Wende das Distributivgesetz an.

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

Schritt 5.2.3.13

Vereinfache.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.13.1

Mutltipliziere $20$ mit $- 25$ .

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

Schritt 5.2.3.13.2

Mutltipliziere $150$ mit $- 25$ .

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

Schritt 5.2.3.13.3

Mutltipliziere $500$ mit $- 25$ .

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

Schritt 5.2.3.13.4

Mutltipliziere $- 25$ mit $625$ .

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

Schritt 5.2.3.14

Wende die Produktregel auf $\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$ an.

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

Schritt 5.2.3.15

Potenziere $4$ mit $3$ .

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

Schritt 5.2.3.16

Kürze den gemeinsamen Faktor von $64$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.16.1

Faktorisiere $64$ aus $16000$ heraus.

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

Schritt 5.2.3.16.2

Kürze den gemeinsamen Faktor.

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

Schritt 5.2.3.16.3

Forme den Ausdruck um.

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

Schritt 5.2.3.17

Wende den binomischen Lehrsatz an.

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

Schritt 5.2.3.18

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.18.1

Multipliziere die Exponenten in ${({(x - 9)}^{\frac{1}{5}})}^{3}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.18.1.1

Wende die Potenzregel an und multipliziere die Exponenten, ${(a^{m})}^{n} = a^{m n}$ .

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

Schritt 5.2.3.18.1.2

Kombiniere $\frac{1}{5}$ und $3$ .

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

Schritt 5.2.3.18.2

Multipliziere die Exponenten in ${({(x - 9)}^{\frac{1}{5}})}^{2}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.18.2.1

Wende die Potenzregel an und multipliziere die Exponenten, ${(a^{m})}^{n} = a^{m n}$ .

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

Schritt 5.2.3.18.2.2

Kombiniere $\frac{1}{5}$ und $2$ .

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

Schritt 5.2.3.18.3

Mutltipliziere $5$ mit $3$ .

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

Schritt 5.2.3.18.4

Potenziere $5$ mit $2$ .

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

Schritt 5.2.3.18.5

Mutltipliziere $25$ mit $3$ .

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

Schritt 5.2.3.18.6

Potenziere $5$ mit $3$ .

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

Schritt 5.2.3.19

Wende das Distributivgesetz an.

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

Schritt 5.2.3.20

Vereinfache.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.20.1

Mutltipliziere $15$ mit $250$ .

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

Schritt 5.2.3.20.2

Mutltipliziere $75$ mit $250$ .

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

Schritt 5.2.3.20.3

Mutltipliziere $250$ mit $125$ .

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

Schritt 5.2.3.21

Wende die Produktregel auf $\frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$ an.

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

Schritt 5.2.3.22

Potenziere $4$ mit $2$ .

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

Schritt 5.2.3.23

Kürze den gemeinsamen Faktor von $16$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.23.1

Faktorisiere $16$ aus $- 20000$ heraus.

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

Schritt 5.2.3.23.2

Kürze den gemeinsamen Faktor.

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

Schritt 5.2.3.23.3

Forme den Ausdruck um.

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

Schritt 5.2.3.24

Schreibe ${({(x - 9)}^{\frac{1}{5}} + 5)}^{2}$ als $({(x - 9)}^{\frac{1}{5}} + 5) ({(x - 9)}^{\frac{1}{5}} + 5)$ um.

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

Schritt 5.2.3.25

Multipliziere $({(x - 9)}^{\frac{1}{5}} + 5) ({(x - 9)}^{\frac{1}{5}} + 5)$ aus unter Verwendung der FOIL-Methode.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.25.1

Wende das Distributivgesetz an.

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

Schritt 5.2.3.25.2

Wende das Distributivgesetz an.

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

Schritt 5.2.3.25.3

Wende das Distributivgesetz an.

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

Schritt 5.2.3.26

Vereinfache und fasse gleichartige Terme zusammen.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.26.1

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.26.1.1

Multipliziere ${(x - 9)}^{\frac{1}{5}}$ mit ${(x - 9)}^{\frac{1}{5}}$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.26.1.1.1

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 5.2.3.26.1.1.2

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 5.2.3.26.1.1.3

Addiere $1$ und $1$ .

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

Schritt 5.2.3.26.1.2

Bringe $5$ auf die linke Seite von ${(x - 9)}^{\frac{1}{5}}$ .

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

Schritt 5.2.3.26.1.3

Mutltipliziere $5$ mit $5$ .

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

Schritt 5.2.3.26.2

Addiere $5 {(x - 9)}^{\frac{1}{5}}$ und $5 {(x - 9)}^{\frac{1}{5}}$ .

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

Schritt 5.2.3.27

Wende das Distributivgesetz an.

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

Schritt 5.2.3.28

Vereinfache.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.28.1

Mutltipliziere $10$ mit $- 1250$ .

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

Schritt 5.2.3.28.2

Mutltipliziere $- 1250$ mit $25$ .

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

Schritt 5.2.3.29

Kürze den gemeinsamen Faktor von $4$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.3.29.1

Faktorisiere $4$ aus $12500$ heraus.

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

Schritt 5.2.3.29.2

Kürze den gemeinsamen Faktor.

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

Schritt 5.2.3.29.3

Forme den Ausdruck um.

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

Schritt 5.2.3.30

Wende das Distributivgesetz an.

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

Schritt 5.2.3.31

Mutltipliziere $3125$ mit $5$ .

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

Schritt 5.2.4

Vereinfache durch Addieren von Termen.

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.4.1

Vereine die Terme mit entgegengesetztem Vorzeichen in $x + 25 {(x - 9)}^{\frac{4}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 1250 {(x - 9)}^{\frac{2}{5}} + 3125 {(x - 9)}^{\frac{1}{5}} + 3116 - 25 {(x - 9)}^{\frac{4}{5}} - 500 {(x - 9)}^{\frac{3}{5}} - 3750 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 15625 + 250 {(x - 9)}^{\frac{3}{5}} + 3750 {(x - 9)}^{\frac{2}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} + 31250 - 1250 {(x - 9)}^{\frac{2}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} - 31250 + 3125 {(x - 9)}^{\frac{1}{5}} + 15625 - 3116$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.4.1.1

Subtrahiere $25 {(x - 9)}^{\frac{4}{5}}$ von $25 {(x - 9)}^{\frac{4}{5}}$ .

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

Schritt 5.2.4.1.2

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

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

Schritt 5.2.4.1.3

Addiere $- 3750 {(x - 9)}^{\frac{2}{5}}$ und $3750 {(x - 9)}^{\frac{2}{5}}$ .

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

Schritt 5.2.4.1.4

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

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

Schritt 5.2.4.1.5

Subtrahiere $1250 {(x - 9)}^{\frac{2}{5}}$ von $1250 {(x - 9)}^{\frac{2}{5}}$ .

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

Schritt 5.2.4.1.6

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

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

Schritt 5.2.4.1.7

Subtrahiere $31250$ von $31250$ .

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

Schritt 5.2.4.1.8

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

Schritt 5.2.4.1.9

Addiere $- 15625$ und $15625$ .

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

Schritt 5.2.4.1.10

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

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

Schritt 5.2.4.1.11

Subtrahiere $3116$ von $3116$ .

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

Schritt 5.2.4.1.12

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

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

Schritt 5.2.4.2

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

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

Schritt 5.2.4.3

Vereine die Terme mit entgegengesetztem Vorzeichen in $x + 3125 {(x - 9)}^{\frac{1}{5}} - 250 {(x - 9)}^{\frac{3}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 250 {(x - 9)}^{\frac{3}{5}} + 18750 {(x - 9)}^{\frac{1}{5}} - 12500 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.4.3.1

Addiere $- 250 {(x - 9)}^{\frac{3}{5}}$ und $250 {(x - 9)}^{\frac{3}{5}}$ .

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

Schritt 5.2.4.3.2

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

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

Schritt 5.2.4.4

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

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

Schritt 5.2.4.5

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

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

Schritt 5.2.4.6

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

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

Schritt 5.2.4.7

Vereine die Terme mit entgegengesetztem Vorzeichen in $x - 3125 {(x - 9)}^{\frac{1}{5}} + 3125 {(x - 9)}^{\frac{1}{5}}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.2.4.7.1

Addiere $- 3125 {(x - 9)}^{\frac{1}{5}}$ und $3125 {(x - 9)}^{\frac{1}{5}}$ .

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

Schritt 5.2.4.7.2

Addiere $x$ und $0$ .

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

Schritt 5.3

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

Tippen, um mehr Schritte zu sehen ...

Schritt 5.3.1

Bilde die verkettete Ergebnisfunktion.

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

Schritt 5.3.2

Berechne $f (1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3116)$ durch Einsetzen des Wertes von $f^{- 1}$ in $f$ .

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

Schritt 5.3.3

Subtrahiere $9$ von $- 3116$ .

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

Schritt 5.4

Da $f^{- 1} (f (x)) = x$ und $f (f^{- 1} (x)) = x$ gleich sind, ist $f^{- 1} (x) = 1024 x^{5} - 6400 x^{4} + 16000 x^{3} - 20000 x^{2} + 12500 x - 3116$ die inverse Funktion (Umkehrfunktion) von $f (x) = \frac{{(x - 9)}^{\frac{1}{5}} + 5}{4}$ .

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