Aljabar Contoh

$f (x) = 5 x^{\frac{1}{5}} + 3$

Langkah 1

Tuliskan $f (x) = 5 x^{\frac{1}{5}} + 3$ sebagai sebuah persamaan.

$y = 5 x^{\frac{1}{5}} + 3$

Langkah 2

Saling tukar variabel.

$x = 5 y^{\frac{1}{5}} + 3$

Langkah 3

Selesaikan $y$ .

Ketuk untuk lebih banyak langkah...

Langkah 3.1

Tulis kembali persamaan tersebut sebagai $5 y^{\frac{1}{5}} + 3 = x$ .

$5 y^{\frac{1}{5}} + 3 = x$

Langkah 3.2

Pindahkan semua suku yang tidak mengandung $y$ ke sisi kanan dari persamaan.

Ketuk untuk lebih banyak langkah...

Langkah 3.2.1

Kurangkan $3$ dari kedua sisi persamaan tersebut.

$5 y^{\frac{1}{5}} - x = - 3$

Langkah 3.2.2

Tambahkan $x$ ke kedua sisi persamaan.

$5 y^{\frac{1}{5}} = - 3 + x$

Langkah 3.3

Pangkatkan setiap sisi persamaan dengan pangkat $5$ untuk menghilangkan eksponen pecahan di sisi kiri.

${(5 y^{\frac{1}{5}})}^{5} = {(- 3 + x)}^{5}$

Langkah 3.4

Sederhanakan bentuk eksponen.

Ketuk untuk lebih banyak langkah...

Langkah 3.4.1

Sederhanakan sisi kirinya.

Ketuk untuk lebih banyak langkah...

Langkah 3.4.1.1

Sederhanakan ${(5 y^{\frac{1}{5}})}^{5}$ .

Ketuk untuk lebih banyak langkah...

Langkah 3.4.1.1.1

Terapkan kaidah hasil kali ke $5 y^{\frac{1}{5}}$ .

$5^{5} {(y^{\frac{1}{5}})}^{5} = {(- 3 + x)}^{5}$

Langkah 3.4.1.1.2

Naikkan $5$ menjadi pangkat $5$ .

$3125 {(y^{\frac{1}{5}})}^{5} = {(- 3 + x)}^{5}$

Langkah 3.4.1.1.3

Kalikan eksponen dalam ${(y^{\frac{1}{5}})}^{5}$ .

Ketuk untuk lebih banyak langkah...

Langkah 3.4.1.1.3.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$3125 y^{\frac{1}{5} \cdot 5} = {(- 3 + x)}^{5}$

Langkah 3.4.1.1.3.2

Batalkan faktor persekutuan dari $5$ .

Ketuk untuk lebih banyak langkah...

Langkah 3.4.1.1.3.2.1

Batalkan faktor persekutuan.

$3125 y^{\frac{1}{5} \cdot 5} = {(- 3 + x)}^{5}$

Langkah 3.4.1.1.3.2.2

Tulis kembali pernyataannya.

$3125 y^{1} = {(- 3 + x)}^{5}$

Langkah 3.4.1.1.4

Sederhanakan.

$3125 y = {(- 3 + x)}^{5}$

Langkah 3.4.2

Sederhanakan sisi kanannya.

Ketuk untuk lebih banyak langkah...

Langkah 3.4.2.1

Sederhanakan ${(- 3 + x)}^{5}$ .

Ketuk untuk lebih banyak langkah...

Langkah 3.4.2.1.1

Gunakan Teorema Binomial.

$3125 y = {(- 3)}^{5} + 5 {(- 3)}^{4} x + 10 {(- 3)}^{3} x^{2} + 10 {(- 3)}^{2} x^{3} + 5 \cdot - 3 x^{4} + x^{5}$

Langkah 3.4.2.1.2

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 3.4.2.1.2.1

Naikkan $- 3$ menjadi pangkat $5$ .

$3125 y = - 243 + 5 {(- 3)}^{4} x + 10 {(- 3)}^{3} x^{2} + 10 {(- 3)}^{2} x^{3} + 5 \cdot - 3 x^{4} + x^{5}$

Langkah 3.4.2.1.2.2

Naikkan $- 3$ menjadi pangkat $4$ .

$3125 y = - 243 + 5 \cdot 81 x + 10 {(- 3)}^{3} x^{2} + 10 {(- 3)}^{2} x^{3} + 5 \cdot - 3 x^{4} + x^{5}$

Langkah 3.4.2.1.2.3

Kalikan $5$ dengan $81$ .

$3125 y = - 243 + 405 x + 10 {(- 3)}^{3} x^{2} + 10 {(- 3)}^{2} x^{3} + 5 \cdot - 3 x^{4} + x^{5}$

Langkah 3.4.2.1.2.4

Naikkan $- 3$ menjadi pangkat $3$ .

$3125 y = - 243 + 405 x + 10 \cdot - 27 x^{2} + 10 {(- 3)}^{2} x^{3} + 5 \cdot - 3 x^{4} + x^{5}$

Langkah 3.4.2.1.2.5

Kalikan $10$ dengan $- 27$ .

$3125 y = - 243 + 405 x - 270 x^{2} + 10 {(- 3)}^{2} x^{3} + 5 \cdot - 3 x^{4} + x^{5}$

Langkah 3.4.2.1.2.6

Naikkan $- 3$ menjadi pangkat $2$ .

$3125 y = - 243 + 405 x - 270 x^{2} + 10 \cdot 9 x^{3} + 5 \cdot - 3 x^{4} + x^{5}$

Langkah 3.4.2.1.2.7

Kalikan $10$ dengan $9$ .

$3125 y = - 243 + 405 x - 270 x^{2} + 90 x^{3} + 5 \cdot - 3 x^{4} + x^{5}$

Langkah 3.4.2.1.2.8

Kalikan $5$ dengan $- 3$ .

$3125 y = - 243 + 405 x - 270 x^{2} + 90 x^{3} - 15 x^{4} + x^{5}$

Langkah 3.5

Bagi setiap suku pada $3125 y = - 243 + 405 x - 270 x^{2} + 90 x^{3} - 15 x^{4} + x^{5}$ dengan $3125$ dan sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 3.5.1

Bagilah setiap suku di $3125 y = - 243 + 405 x - 270 x^{2} + 90 x^{3} - 15 x^{4} + x^{5}$ dengan $3125$ .

$\frac{3125 y}{3125} = \frac{- 243}{3125} + \frac{405 x}{3125} + \frac{- 270 x^{2}}{3125} + \frac{90 x^{3}}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.2

Sederhanakan sisi kirinya.

Ketuk untuk lebih banyak langkah...

Langkah 3.5.2.1

Batalkan faktor persekutuan dari $3125$ .

Ketuk untuk lebih banyak langkah...

Langkah 3.5.2.1.1

Batalkan faktor persekutuan.

$\frac{3125 y}{3125} = \frac{- 243}{3125} + \frac{405 x}{3125} + \frac{- 270 x^{2}}{3125} + \frac{90 x^{3}}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.2.1.2

Bagilah $y$ dengan $1$ .

$y = \frac{- 243}{3125} + \frac{405 x}{3125} + \frac{- 270 x^{2}}{3125} + \frac{90 x^{3}}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3

Sederhanakan sisi kanannya.

Ketuk untuk lebih banyak langkah...

Langkah 3.5.3.1

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 3.5.3.1.1

Pindahkan tanda negatif di depan pecahan.

$y = - \frac{243}{3125} + \frac{405 x}{3125} + \frac{- 270 x^{2}}{3125} + \frac{90 x^{3}}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.2

Hapus faktor persekutuan dari $405$ dan $3125$ .

Ketuk untuk lebih banyak langkah...

Langkah 3.5.3.1.2.1

Faktorkan $5$ dari $405 x$ .

$y = - \frac{243}{3125} + \frac{5 (81 x)}{3125} + \frac{- 270 x^{2}}{3125} + \frac{90 x^{3}}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.2.2

Batalkan faktor persekutuan.

Ketuk untuk lebih banyak langkah...

Langkah 3.5.3.1.2.2.1

Faktorkan $5$ dari $3125$ .

$y = - \frac{243}{3125} + \frac{5 (81 x)}{5 (625)} + \frac{- 270 x^{2}}{3125} + \frac{90 x^{3}}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.2.2.2

Batalkan faktor persekutuan.

$y = - \frac{243}{3125} + \frac{5 (81 x)}{5 \cdot 625} + \frac{- 270 x^{2}}{3125} + \frac{90 x^{3}}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.2.2.3

Tulis kembali pernyataannya.

$y = - \frac{243}{3125} + \frac{81 x}{625} + \frac{- 270 x^{2}}{3125} + \frac{90 x^{3}}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.3

Hapus faktor persekutuan dari $- 270$ dan $3125$ .

Ketuk untuk lebih banyak langkah...

Langkah 3.5.3.1.3.1

Faktorkan $5$ dari $- 270 x^{2}$ .

$y = - \frac{243}{3125} + \frac{81 x}{625} + \frac{5 (- 54 x^{2})}{3125} + \frac{90 x^{3}}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.3.2

Batalkan faktor persekutuan.

Ketuk untuk lebih banyak langkah...

Langkah 3.5.3.1.3.2.1

Faktorkan $5$ dari $3125$ .

$y = - \frac{243}{3125} + \frac{81 x}{625} + \frac{5 (- 54 x^{2})}{5 (625)} + \frac{90 x^{3}}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.3.2.2

Batalkan faktor persekutuan.

$y = - \frac{243}{3125} + \frac{81 x}{625} + \frac{5 (- 54 x^{2})}{5 \cdot 625} + \frac{90 x^{3}}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.3.2.3

Tulis kembali pernyataannya.

$y = - \frac{243}{3125} + \frac{81 x}{625} + \frac{- 54 x^{2}}{625} + \frac{90 x^{3}}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.4

Pindahkan tanda negatif di depan pecahan.

$y = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{90 x^{3}}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.5

Hapus faktor persekutuan dari $90$ dan $3125$ .

Ketuk untuk lebih banyak langkah...

Langkah 3.5.3.1.5.1

Faktorkan $5$ dari $90 x^{3}$ .

$y = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{5 (18 x^{3})}{3125} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.5.2

Batalkan faktor persekutuan.

Ketuk untuk lebih banyak langkah...

Langkah 3.5.3.1.5.2.1

Faktorkan $5$ dari $3125$ .

$y = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{5 (18 x^{3})}{5 (625)} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.5.2.2

Batalkan faktor persekutuan.

$y = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{5 (18 x^{3})}{5 \cdot 625} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.5.2.3

Tulis kembali pernyataannya.

$y = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} + \frac{- 15 x^{4}}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.6

Hapus faktor persekutuan dari $- 15$ dan $3125$ .

Ketuk untuk lebih banyak langkah...

Langkah 3.5.3.1.6.1

Faktorkan $5$ dari $- 15 x^{4}$ .

$y = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} + \frac{5 (- 3 x^{4})}{3125} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.6.2

Batalkan faktor persekutuan.

Ketuk untuk lebih banyak langkah...

Langkah 3.5.3.1.6.2.1

Faktorkan $5$ dari $3125$ .

$y = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} + \frac{5 (- 3 x^{4})}{5 (625)} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.6.2.2

Batalkan faktor persekutuan.

$y = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} + \frac{5 (- 3 x^{4})}{5 \cdot 625} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.6.2.3

Tulis kembali pernyataannya.

$y = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} + \frac{- 3 x^{4}}{625} + \frac{x^{5}}{3125}$

Langkah 3.5.3.1.7

Pindahkan tanda negatif di depan pecahan.

$y = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125}$

Langkah 4

Ganti $y$ dengan $f^{- 1} (x)$ untuk memunculkan jawaban akhir.

$f^{- 1} (x) = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125}$

Langkah 5

Periksa apakah $f^{- 1} (x) = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125}$ merupakan balikan dari $f (x) = 5 x^{\frac{1}{5}} + 3$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.1

Untuk memverifikasi balikannya, periksa apakah $f^{- 1} (f (x)) = x$ dan $f (f^{- 1} (x)) = x$ .

Langkah 5.2

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

Ketuk untuk lebih banyak langkah...

Langkah 5.2.1

Tulis fungsi hasil komposit.

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

Langkah 5.2.2

Evaluasi $f^{- 1} (5 x^{\frac{1}{5}} + 3)$ dengan mensubstitusikan nilai (Variabel1) ke dalam (Variabel2).

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = - \frac{243}{3125} + \frac{81 (5 x^{\frac{1}{5}} + 3)}{625} - \frac{54 {(5 x^{\frac{1}{5}} + 3)}^{2}}{625} + \frac{18 {(5 x^{\frac{1}{5}} + 3)}^{3}}{625} - \frac{3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125}$

Langkah 5.2.3

Gabungkan pembilang dari penyebut persekutuan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{81 (5 x^{\frac{1}{5}} + 3) - 54 {(5 x^{\frac{1}{5}} + 3)}^{2} + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.1

Terapkan sifat distributif.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{81 (5 x^{\frac{1}{5}}) + 81 \cdot 3 - 54 {(5 x^{\frac{1}{5}} + 3)}^{2} + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.2

Kalikan $5$ dengan $81$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 81 \cdot 3 - 54 {(5 x^{\frac{1}{5}} + 3)}^{2} + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.3

Kalikan $81$ dengan $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 {(5 x^{\frac{1}{5}} + 3)}^{2} + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.4

Tulis kembali ${(5 x^{\frac{1}{5}} + 3)}^{2}$ sebagai $(5 x^{\frac{1}{5}} + 3) (5 x^{\frac{1}{5}} + 3)$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 ((5 x^{\frac{1}{5}} + 3) (5 x^{\frac{1}{5}} + 3)) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.5

Perluas $(5 x^{\frac{1}{5}} + 3) (5 x^{\frac{1}{5}} + 3)$ menggunakan Metode FOIL.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.5.1

Terapkan sifat distributif.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (5 x^{\frac{1}{5}} (5 x^{\frac{1}{5}} + 3) + 3 (5 x^{\frac{1}{5}} + 3)) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.5.2

Terapkan sifat distributif.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (5 x^{\frac{1}{5}} (5 x^{\frac{1}{5}}) + 5 x^{\frac{1}{5}} \cdot 3 + 3 (5 x^{\frac{1}{5}} + 3)) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.5.3

Terapkan sifat distributif.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (5 x^{\frac{1}{5}} (5 x^{\frac{1}{5}}) + 5 x^{\frac{1}{5}} \cdot 3 + 3 (5 x^{\frac{1}{5}}) + 3 \cdot 3) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.6

Sederhanakan dan gabungkan suku-suku sejenis.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.6.1

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.6.1.1

Tulis kembali menggunakan sifat komutatif dari perkalian.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (5 \cdot (5 x^{\frac{1}{5}} x^{\frac{1}{5}}) + 5 x^{\frac{1}{5}} \cdot 3 + 3 (5 x^{\frac{1}{5}}) + 3 \cdot 3) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.6.1.2

Kalikan $x^{\frac{1}{5}}$ dengan $x^{\frac{1}{5}}$ dengan menambahkan eksponennya.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.6.1.2.1

Pindahkan $x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (5 \cdot (5 (x^{\frac{1}{5}} x^{\frac{1}{5}})) + 5 x^{\frac{1}{5}} \cdot 3 + 3 (5 x^{\frac{1}{5}}) + 3 \cdot 3) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.6.1.2.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (5 \cdot (5 x^{\frac{1}{5} + \frac{1}{5}}) + 5 x^{\frac{1}{5}} \cdot 3 + 3 (5 x^{\frac{1}{5}}) + 3 \cdot 3) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.6.1.2.3

Gabungkan pembilang dari penyebut persekutuan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (5 \cdot (5 x^{\frac{1 + 1}{5}}) + 5 x^{\frac{1}{5}} \cdot 3 + 3 (5 x^{\frac{1}{5}}) + 3 \cdot 3) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.6.1.2.4

Tambahkan $1$ dan $1$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (5 \cdot (5 x^{\frac{2}{5}}) + 5 x^{\frac{1}{5}} \cdot 3 + 3 (5 x^{\frac{1}{5}}) + 3 \cdot 3) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.6.1.3

Kalikan $5$ dengan $5$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (25 x^{\frac{2}{5}} + 5 x^{\frac{1}{5}} \cdot 3 + 3 (5 x^{\frac{1}{5}}) + 3 \cdot 3) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.6.1.4

Kalikan $3$ dengan $5$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (25 x^{\frac{2}{5}} + 15 x^{\frac{1}{5}} + 3 (5 x^{\frac{1}{5}}) + 3 \cdot 3) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.6.1.5

Kalikan $5$ dengan $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (25 x^{\frac{2}{5}} + 15 x^{\frac{1}{5}} + 15 x^{\frac{1}{5}} + 3 \cdot 3) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.6.1.6

Kalikan $3$ dengan $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (25 x^{\frac{2}{5}} + 15 x^{\frac{1}{5}} + 15 x^{\frac{1}{5}} + 9) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.6.2

Tambahkan $15 x^{\frac{1}{5}}$ dan $15 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (25 x^{\frac{2}{5}} + 30 x^{\frac{1}{5}} + 9) + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.7

Terapkan sifat distributif.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 54 (25 x^{\frac{2}{5}}) - 54 (30 x^{\frac{1}{5}}) - 54 \cdot 9 + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.8

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.8.1

Kalikan $25$ dengan $- 54$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 54 (30 x^{\frac{1}{5}}) - 54 \cdot 9 + 18 {(5 x^{\frac{1}{5}} + 3)}^{3} - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.8.2

Kalikan $30$ dengan $- 54$ .

Langkah 5.2.4.8.3

Kalikan $- 54$ dengan $9$ .

Langkah 5.2.4.9

Gunakan Teorema Binomial.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 ({(5 x^{\frac{1}{5}})}^{3} + 3 {(5 x^{\frac{1}{5}})}^{2} \cdot 3 + 3 (5 x^{\frac{1}{5}}) \cdot 3^{2} + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.10.1

Terapkan kaidah hasil kali ke $5 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (5^{3} {(x^{\frac{1}{5}})}^{3} + 3 {(5 x^{\frac{1}{5}})}^{2} \cdot 3 + 3 (5 x^{\frac{1}{5}}) \cdot 3^{2} + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.2

Naikkan $5$ menjadi pangkat $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 {(x^{\frac{1}{5}})}^{3} + 3 {(5 x^{\frac{1}{5}})}^{2} \cdot 3 + 3 (5 x^{\frac{1}{5}}) \cdot 3^{2} + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.3

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{3}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.10.3.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{1}{5} \cdot 3} + 3 {(5 x^{\frac{1}{5}})}^{2} \cdot 3 + 3 (5 x^{\frac{1}{5}}) \cdot 3^{2} + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.3.2

Gabungkan $\frac{1}{5}$ dan $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 3 {(5 x^{\frac{1}{5}})}^{2} \cdot 3 + 3 (5 x^{\frac{1}{5}}) \cdot 3^{2} + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.4

Terapkan kaidah hasil kali ke $5 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 3 (5^{2} {(x^{\frac{1}{5}})}^{2}) \cdot 3 + 3 (5 x^{\frac{1}{5}}) \cdot 3^{2} + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.5

Naikkan $5$ menjadi pangkat $2$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 3 (25 {(x^{\frac{1}{5}})}^{2}) \cdot 3 + 3 (5 x^{\frac{1}{5}}) \cdot 3^{2} + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.6

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{2}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.10.6.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 3 (25 x^{\frac{1}{5} \cdot 2}) \cdot 3 + 3 (5 x^{\frac{1}{5}}) \cdot 3^{2} + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.6.2

Gabungkan $\frac{1}{5}$ dan $2$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 3 (25 x^{\frac{2}{5}}) \cdot 3 + 3 (5 x^{\frac{1}{5}}) \cdot 3^{2} + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.7

Kalikan $25$ dengan $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 75 x^{\frac{2}{5}} \cdot 3 + 3 (5 x^{\frac{1}{5}}) \cdot 3^{2} + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.8

Kalikan $3$ dengan $75$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 225 x^{\frac{2}{5}} + 3 (5 x^{\frac{1}{5}}) \cdot 3^{2} + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.9

Kalikan $3$ dengan $3^{2}$ dengan menambahkan eksponennya.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.10.9.1

Pindahkan $3^{2}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 225 x^{\frac{2}{5}} + 3^{2} \cdot (3 (5 x^{\frac{1}{5}})) + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.9.2

Kalikan $3^{2}$ dengan $3$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.10.9.2.1

Naikkan $3$ menjadi pangkat $1$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 225 x^{\frac{2}{5}} + 3^{2} \cdot (3 (5 x^{\frac{1}{5}})) + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.9.2.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 225 x^{\frac{2}{5}} + 3^{2 + 1} (5 x^{\frac{1}{5}}) + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.9.3

Tambahkan $2$ dan $1$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 225 x^{\frac{2}{5}} + 3^{3} (5 x^{\frac{1}{5}}) + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.10

Naikkan $3$ menjadi pangkat $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 225 x^{\frac{2}{5}} + 27 (5 x^{\frac{1}{5}}) + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.11

Kalikan $5$ dengan $27$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 225 x^{\frac{2}{5}} + 135 x^{\frac{1}{5}} + 3^{3}) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.10.12

Naikkan $3$ menjadi pangkat $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}} + 225 x^{\frac{2}{5}} + 135 x^{\frac{1}{5}} + 27) - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.11

Terapkan sifat distributif.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 18 (125 x^{\frac{3}{5}}) + 18 (225 x^{\frac{2}{5}}) + 18 (135 x^{\frac{1}{5}}) + 18 \cdot 27 - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.12

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.12.1

Kalikan $125$ dengan $18$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 18 (225 x^{\frac{2}{5}}) + 18 (135 x^{\frac{1}{5}}) + 18 \cdot 27 - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.12.2

Kalikan $225$ dengan $18$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 18 (135 x^{\frac{1}{5}}) + 18 \cdot 27 - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.12.3

Kalikan $135$ dengan $18$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 18 \cdot 27 - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.12.4

Kalikan $18$ dengan $27$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 {(5 x^{\frac{1}{5}} + 3)}^{4}}{625}$

Langkah 5.2.4.13

Gunakan Teorema Binomial.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 ({(5 x^{\frac{1}{5}})}^{4} + 4 {(5 x^{\frac{1}{5}})}^{3} \cdot 3 + 6 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.14.1

Terapkan kaidah hasil kali ke $5 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (5^{4} {(x^{\frac{1}{5}})}^{4} + 4 {(5 x^{\frac{1}{5}})}^{3} \cdot 3 + 6 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.2

Naikkan $5$ menjadi pangkat $4$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 {(x^{\frac{1}{5}})}^{4} + 4 {(5 x^{\frac{1}{5}})}^{3} \cdot 3 + 6 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.3

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{4}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.14.3.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{1}{5} \cdot 4} + 4 {(5 x^{\frac{1}{5}})}^{3} \cdot 3 + 6 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.3.2

Gabungkan $\frac{1}{5}$ dan $4$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 4 {(5 x^{\frac{1}{5}})}^{3} \cdot 3 + 6 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.4

Terapkan kaidah hasil kali ke $5 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 4 (5^{3} {(x^{\frac{1}{5}})}^{3}) \cdot 3 + 6 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.5

Naikkan $5$ menjadi pangkat $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 4 (125 {(x^{\frac{1}{5}})}^{3}) \cdot 3 + 6 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.6

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{3}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.14.6.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 4 (125 x^{\frac{1}{5} \cdot 3}) \cdot 3 + 6 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.6.2

Gabungkan $\frac{1}{5}$ dan $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 4 (125 x^{\frac{3}{5}}) \cdot 3 + 6 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.7

Kalikan $125$ dengan $4$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 500 x^{\frac{3}{5}} \cdot 3 + 6 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.8

Kalikan $3$ dengan $500$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 1500 x^{\frac{3}{5}} + 6 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.9

Terapkan kaidah hasil kali ke $5 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 1500 x^{\frac{3}{5}} + 6 (5^{2} {(x^{\frac{1}{5}})}^{2}) \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.10

Naikkan $5$ menjadi pangkat $2$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 1500 x^{\frac{3}{5}} + 6 (25 {(x^{\frac{1}{5}})}^{2}) \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.11

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{2}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.14.11.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 1500 x^{\frac{3}{5}} + 6 (25 x^{\frac{1}{5} \cdot 2}) \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.11.2

Gabungkan $\frac{1}{5}$ dan $2$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 1500 x^{\frac{3}{5}} + 6 (25 x^{\frac{2}{5}}) \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.12

Kalikan $25$ dengan $6$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 1500 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}} \cdot 3^{2} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.13

Naikkan $3$ menjadi pangkat $2$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 1500 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}} \cdot 9 + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.14

Kalikan $9$ dengan $150$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 1500 x^{\frac{3}{5}} + 1350 x^{\frac{2}{5}} + 4 (5 x^{\frac{1}{5}}) \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.15

Kalikan $5$ dengan $4$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 1500 x^{\frac{3}{5}} + 1350 x^{\frac{2}{5}} + 20 x^{\frac{1}{5}} \cdot 3^{3} + 3^{4})}{625}$

Langkah 5.2.4.14.16

Naikkan $3$ menjadi pangkat $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 1500 x^{\frac{3}{5}} + 1350 x^{\frac{2}{5}} + 20 x^{\frac{1}{5}} \cdot 27 + 3^{4})}{625}$

Langkah 5.2.4.14.17

Kalikan $27$ dengan $20$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 1500 x^{\frac{3}{5}} + 1350 x^{\frac{2}{5}} + 540 x^{\frac{1}{5}} + 3^{4})}{625}$

Langkah 5.2.4.14.18

Naikkan $3$ menjadi pangkat $4$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}} + 1500 x^{\frac{3}{5}} + 1350 x^{\frac{2}{5}} + 540 x^{\frac{1}{5}} + 81)}{625}$

Langkah 5.2.4.15

Terapkan sifat distributif.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 3 (625 x^{\frac{4}{5}}) - 3 (1500 x^{\frac{3}{5}}) - 3 (1350 x^{\frac{2}{5}}) - 3 (540 x^{\frac{1}{5}}) - 3 \cdot 81}{625}$

Langkah 5.2.4.16

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.4.16.1

Kalikan $625$ dengan $- 3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 1875 x^{\frac{4}{5}} - 3 (1500 x^{\frac{3}{5}}) - 3 (1350 x^{\frac{2}{5}}) - 3 (540 x^{\frac{1}{5}}) - 3 \cdot 81}{625}$

Langkah 5.2.4.16.2

Kalikan $1500$ dengan $- 3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}} - 3 (1350 x^{\frac{2}{5}}) - 3 (540 x^{\frac{1}{5}}) - 3 \cdot 81}{625}$

Langkah 5.2.4.16.3

Kalikan $1350$ dengan $- 3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}} - 4050 x^{\frac{2}{5}} - 3 (540 x^{\frac{1}{5}}) - 3 \cdot 81}{625}$

Langkah 5.2.4.16.4

Kalikan $540$ dengan $- 3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}} - 4050 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 3 \cdot 81}{625}$

Langkah 5.2.4.16.5

Kalikan $- 3$ dengan $81$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}} - 4050 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 243}{625}$

Langkah 5.2.5

Sederhanakan dengan menambahkan suku-suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.5.1

Gabungkan suku balikan dalam $405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 486 + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 486 - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}} - 4050 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 243$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.5.1.1

Tambahkan $- 486$ dan $486$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} + 0 - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}} - 4050 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 243}{625}$

Langkah 5.2.5.1.2

Tambahkan $405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}}$ dan $0$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} + 2250 x^{\frac{3}{5}} + 4050 x^{\frac{2}{5}} + 2430 x^{\frac{1}{5}} - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}} - 4050 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} - 243}{625}$

Langkah 5.2.5.1.3

Kurangi $4050 x^{\frac{2}{5}}$ dengan $4050 x^{\frac{2}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} + 2250 x^{\frac{3}{5}} + 2430 x^{\frac{1}{5}} - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}} + 0 - 1620 x^{\frac{1}{5}} - 243}{625}$

Langkah 5.2.5.1.4

Tambahkan $405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} + 2250 x^{\frac{3}{5}} + 2430 x^{\frac{1}{5}} - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}}$ dan $0$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} + 243 - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} + 2250 x^{\frac{3}{5}} + 2430 x^{\frac{1}{5}} - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}} - 1620 x^{\frac{1}{5}} - 243}{625}$

Langkah 5.2.5.1.5

Kurangi $243$ dengan $243$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{405 x^{\frac{1}{5}} - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} + 2250 x^{\frac{3}{5}} + 2430 x^{\frac{1}{5}} - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}} - 1620 x^{\frac{1}{5}} + 0}{625}$

Langkah 5.2.5.1.6

Tambahkan $405 x^{\frac{1}{5}} - 1350 x^{\frac{2}{5}} - 1620 x^{\frac{1}{5}} + 2250 x^{\frac{3}{5}} + 2430 x^{\frac{1}{5}} - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}} - 1620 x^{\frac{1}{5}}$ dan $0$ .

Langkah 5.2.5.2

Kurangi $1620 x^{\frac{1}{5}}$ dengan $405 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{- 1215 x^{\frac{1}{5}} - 1350 x^{\frac{2}{5}} + 2250 x^{\frac{3}{5}} + 2430 x^{\frac{1}{5}} - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}} - 1620 x^{\frac{1}{5}}}{625}$

Langkah 5.2.5.3

Tambahkan $- 1215 x^{\frac{1}{5}}$ dan $2430 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{1215 x^{\frac{1}{5}} - 1350 x^{\frac{2}{5}} + 2250 x^{\frac{3}{5}} - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}} - 1620 x^{\frac{1}{5}}}{625}$

Langkah 5.2.5.4

Kurangi $1620 x^{\frac{1}{5}}$ dengan $1215 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{- 405 x^{\frac{1}{5}} - 1350 x^{\frac{2}{5}} + 2250 x^{\frac{3}{5}} - 1875 x^{\frac{4}{5}} - 4500 x^{\frac{3}{5}}}{625}$

Langkah 5.2.5.5

Kurangi $4500 x^{\frac{3}{5}}$ dengan $2250 x^{\frac{3}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{- 405 x^{\frac{1}{5}} - 1350 x^{\frac{2}{5}} - 1875 x^{\frac{4}{5}} - 2250 x^{\frac{3}{5}}}{625}$

Langkah 5.2.6

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.6.1

Pindahkan tanda negatif di depan pecahan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = - \frac{243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{- 405 x^{\frac{1}{5}} - 1350 x^{\frac{2}{5}} - 1875 x^{\frac{4}{5}} - 2250 x^{\frac{3}{5}}}{625}$

Langkah 5.2.6.2

Faktorkan $- 15 x^{\frac{1}{5}}$ dari $- 405 x^{\frac{1}{5}} - 1350 x^{\frac{2}{5}} - 1875 x^{\frac{4}{5}} - 2250 x^{\frac{3}{5}}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.6.2.1

Faktorkan $- 15 x^{\frac{1}{5}}$ dari $- 405 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = - \frac{243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{- 15 x^{\frac{1}{5}} \cdot 27 - 1350 x^{\frac{2}{5}} - 1875 x^{\frac{4}{5}} - 2250 x^{\frac{3}{5}}}{625}$

Langkah 5.2.6.2.2

Faktorkan $- 15 x^{\frac{1}{5}}$ dari $- 1350 x^{\frac{2}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = - \frac{243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{- 15 x^{\frac{1}{5}} \cdot 27 - 15 x^{\frac{1}{5}} (90 x^{\frac{1}{5}}) - 1875 x^{\frac{4}{5}} - 2250 x^{\frac{3}{5}}}{625}$

Langkah 5.2.6.2.3

Faktorkan $- 15 x^{\frac{1}{5}}$ dari $- 1875 x^{\frac{4}{5}}$ .

Langkah 5.2.6.2.4

Faktorkan $- 15 x^{\frac{1}{5}}$ dari $- 2250 x^{\frac{3}{5}}$ .

Langkah 5.2.6.2.5

Faktorkan $- 15 x^{\frac{1}{5}}$ dari $- 15 x^{\frac{1}{5}} (27) - 15 x^{\frac{1}{5}} (90 x^{\frac{1}{5}})$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = - \frac{243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{- 15 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}}) - 15 x^{\frac{1}{5}} (125 x^{\frac{3}{5}}) - 15 x^{\frac{1}{5}} (150 x^{\frac{2}{5}})}{625}$

Langkah 5.2.6.2.6

Faktorkan $- 15 x^{\frac{1}{5}}$ dari $- 15 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}}) - 15 x^{\frac{1}{5}} (125 x^{\frac{3}{5}})$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = - \frac{243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{- 15 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}}) - 15 x^{\frac{1}{5}} (150 x^{\frac{2}{5}})}{625}$

Langkah 5.2.6.2.7

Faktorkan $- 15 x^{\frac{1}{5}}$ dari $- 15 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}}) - 15 x^{\frac{1}{5}} (150 x^{\frac{2}{5}})$ .

Langkah 5.2.6.3

Faktorkan $5$ dari $- 15 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = - \frac{243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{5 (- 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}}))}{625}$

Langkah 5.2.6.4

Batalkan faktor persekutuan.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.6.4.1

Faktorkan $5$ dari $625$ .

Langkah 5.2.6.4.2

Batalkan faktor persekutuan.

Langkah 5.2.6.4.3

Tulis kembali pernyataannya.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = - \frac{243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} + \frac{- 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.6.5

Pindahkan tanda negatif di depan pecahan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = - \frac{243}{3125} + \frac{{(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.7

Gabungkan pembilang dari penyebut persekutuan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + {(5 x^{\frac{1}{5}} + 3)}^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.8.1

Sederhanakan pembilangnya.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.8.1.1

Gunakan Teorema Binomial.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + {(5 x^{\frac{1}{5}})}^{5} + 5 {(5 x^{\frac{1}{5}})}^{4} \cdot 3 + 10 {(5 x^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.8.1.2.1

Terapkan kaidah hasil kali ke $5 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 5^{5} {(x^{\frac{1}{5}})}^{5} + 5 {(5 x^{\frac{1}{5}})}^{4} \cdot 3 + 10 {(5 x^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.2

Naikkan $5$ menjadi pangkat $5$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 {(x^{\frac{1}{5}})}^{5} + 5 {(5 x^{\frac{1}{5}})}^{4} \cdot 3 + 10 {(5 x^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.3

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{5}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.8.1.2.3.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x^{\frac{1}{5} \cdot 5} + 5 {(5 x^{\frac{1}{5}})}^{4} \cdot 3 + 10 {(5 x^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.3.2

Batalkan faktor persekutuan dari $5$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.8.1.2.3.2.1

Batalkan faktor persekutuan.

Langkah 5.2.8.1.2.3.2.2

Tulis kembali pernyataannya.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 5 {(5 x^{\frac{1}{5}})}^{4} \cdot 3 + 10 {(5 x^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.4

Sederhanakan.

Langkah 5.2.8.1.2.5

Terapkan kaidah hasil kali ke $5 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 5 (5^{4} {(x^{\frac{1}{5}})}^{4}) \cdot 3 + 10 {(5 x^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.6

Kalikan $5$ dengan $5^{4}$ dengan menambahkan eksponennya.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.8.1.2.6.1

Pindahkan $5^{4}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 5^{4} \cdot (5 {(x^{\frac{1}{5}})}^{4}) \cdot 3 + 10 {(5 x^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.6.2

Kalikan $5^{4}$ dengan $5$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.8.1.2.6.2.1

Naikkan $5$ menjadi pangkat $1$ .

Langkah 5.2.8.1.2.6.2.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 5^{4 + 1} {(x^{\frac{1}{5}})}^{4} \cdot 3 + 10 {(5 x^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.6.3

Tambahkan $4$ dan $1$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 5^{5} {(x^{\frac{1}{5}})}^{4} \cdot 3 + 10 {(5 x^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.7

Naikkan $5$ menjadi pangkat $5$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 3125 {(x^{\frac{1}{5}})}^{4} \cdot 3 + 10 {(5 x^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.8

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{4}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.8.1.2.8.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 3125 x^{\frac{1}{5} \cdot 4} \cdot 3 + 10 {(5 x^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.8.2

Gabungkan $\frac{1}{5}$ dan $4$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 3125 x^{\frac{4}{5}} \cdot 3 + 10 {(5 x^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.9

Kalikan $3$ dengan $3125$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 10 {(5 x^{\frac{1}{5}})}^{3} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.10

Terapkan kaidah hasil kali ke $5 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 10 (5^{3} {(x^{\frac{1}{5}})}^{3}) \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.11

Naikkan $5$ menjadi pangkat $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 10 (125 {(x^{\frac{1}{5}})}^{3}) \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.12

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{3}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.8.1.2.12.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 10 (125 x^{\frac{1}{5} \cdot 3}) \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.12.2

Gabungkan $\frac{1}{5}$ dan $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 10 (125 x^{\frac{3}{5}}) \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.13

Kalikan $125$ dengan $10$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 1250 x^{\frac{3}{5}} \cdot 3^{2} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.14

Naikkan $3$ menjadi pangkat $2$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 1250 x^{\frac{3}{5}} \cdot 9 + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.15

Kalikan $9$ dengan $1250$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 10 {(5 x^{\frac{1}{5}})}^{2} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.16

Terapkan kaidah hasil kali ke $5 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 10 (5^{2} {(x^{\frac{1}{5}})}^{2}) \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.17

Naikkan $5$ menjadi pangkat $2$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 10 (25 {(x^{\frac{1}{5}})}^{2}) \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.18

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{2}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.8.1.2.18.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 10 (25 x^{\frac{1}{5} \cdot 2}) \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.18.2

Gabungkan $\frac{1}{5}$ dan $2$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 10 (25 x^{\frac{2}{5}}) \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.19

Kalikan $25$ dengan $10$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 250 x^{\frac{2}{5}} \cdot 3^{3} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.20

Naikkan $3$ menjadi pangkat $3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 250 x^{\frac{2}{5}} \cdot 27 + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.21

Kalikan $27$ dengan $250$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 6750 x^{\frac{2}{5}} + 5 (5 x^{\frac{1}{5}}) \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.22

Kalikan $5$ dengan $5$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 6750 x^{\frac{2}{5}} + 25 x^{\frac{1}{5}} \cdot 3^{4} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.23

Naikkan $3$ menjadi pangkat $4$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 6750 x^{\frac{2}{5}} + 25 x^{\frac{1}{5}} \cdot 81 + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.24

Kalikan $81$ dengan $25$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 6750 x^{\frac{2}{5}} + 2025 x^{\frac{1}{5}} + 3^{5}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.2.25

Naikkan $3$ menjadi pangkat $5$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{- 243 + 3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 6750 x^{\frac{2}{5}} + 2025 x^{\frac{1}{5}} + 243}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.3

Tambahkan $- 243$ dan $243$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 6750 x^{\frac{2}{5}} + 2025 x^{\frac{1}{5}} + 0}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.4

Tambahkan $3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 6750 x^{\frac{2}{5}} + 2025 x^{\frac{1}{5}}$ dan $0$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{3125 x + 9375 x^{\frac{4}{5}} + 11250 x^{\frac{3}{5}} + 6750 x^{\frac{2}{5}} + 2025 x^{\frac{1}{5}}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.5

Susun kembali suku-suku.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{3125 x + 11250 x^{\frac{3}{5}} + 9375 x^{\frac{4}{5}} + 6750 x^{\frac{2}{5}} + 2025 x^{\frac{1}{5}}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.6

Tulis kembali $3125 x + 11250 x^{\frac{3}{5}} + 9375 x^{\frac{4}{5}} + 6750 x^{\frac{2}{5}} + 2025 x^{\frac{1}{5}}$ dalam bentuk faktor.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.8.1.6.1

Faktorkan $25 x^{\frac{1}{5}}$ dari $3125 x + 11250 x^{\frac{3}{5}} + 9375 x^{\frac{4}{5}} + 6750 x^{\frac{2}{5}} + 2025 x^{\frac{1}{5}}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.8.1.6.1.1

Faktorkan $25 x^{\frac{1}{5}}$ dari $3125 x$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{25 x^{\frac{1}{5}} (125 x^{\frac{4}{5}}) + 11250 x^{\frac{3}{5}} + 9375 x^{\frac{4}{5}} + 6750 x^{\frac{2}{5}} + 2025 x^{\frac{1}{5}}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.6.1.2

Faktorkan $25 x^{\frac{1}{5}}$ dari $11250 x^{\frac{3}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{25 x^{\frac{1}{5}} (125 x^{\frac{4}{5}}) + 25 x^{\frac{1}{5}} (450 x^{\frac{2}{5}}) + 9375 x^{\frac{4}{5}} + 6750 x^{\frac{2}{5}} + 2025 x^{\frac{1}{5}}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.6.1.3

Faktorkan $25 x^{\frac{1}{5}}$ dari $9375 x^{\frac{4}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{25 x^{\frac{1}{5}} (125 x^{\frac{4}{5}}) + 25 x^{\frac{1}{5}} (450 x^{\frac{2}{5}}) + 25 x^{\frac{1}{5}} (375 x^{\frac{3}{5}}) + 6750 x^{\frac{2}{5}} + 2025 x^{\frac{1}{5}}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.6.1.4

Faktorkan $25 x^{\frac{1}{5}}$ dari $6750 x^{\frac{2}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{25 x^{\frac{1}{5}} (125 x^{\frac{4}{5}}) + 25 x^{\frac{1}{5}} (450 x^{\frac{2}{5}}) + 25 x^{\frac{1}{5}} (375 x^{\frac{3}{5}}) + 25 x^{\frac{1}{5}} (270 x^{\frac{1}{5}}) + 2025 x^{\frac{1}{5}}}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.6.1.5

Faktorkan $25 x^{\frac{1}{5}}$ dari $2025 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{25 x^{\frac{1}{5}} (125 x^{\frac{4}{5}}) + 25 x^{\frac{1}{5}} (450 x^{\frac{2}{5}}) + 25 x^{\frac{1}{5}} (375 x^{\frac{3}{5}}) + 25 x^{\frac{1}{5}} (270 x^{\frac{1}{5}}) + 25 x^{\frac{1}{5}} (81)}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.6.1.6

Faktorkan $25 x^{\frac{1}{5}}$ dari $25 x^{\frac{1}{5}} (125 x^{\frac{4}{5}}) + 25 x^{\frac{1}{5}} (450 x^{\frac{2}{5}})$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{25 x^{\frac{1}{5}} (125 x^{\frac{4}{5}} + 450 x^{\frac{2}{5}}) + 25 x^{\frac{1}{5}} (375 x^{\frac{3}{5}}) + 25 x^{\frac{1}{5}} (270 x^{\frac{1}{5}}) + 25 x^{\frac{1}{5}} (81)}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.6.1.7

Faktorkan $25 x^{\frac{1}{5}}$ dari $25 x^{\frac{1}{5}} (125 x^{\frac{4}{5}} + 450 x^{\frac{2}{5}}) + 25 x^{\frac{1}{5}} (375 x^{\frac{3}{5}})$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{25 x^{\frac{1}{5}} (125 x^{\frac{4}{5}} + 450 x^{\frac{2}{5}} + 375 x^{\frac{3}{5}}) + 25 x^{\frac{1}{5}} (270 x^{\frac{1}{5}}) + 25 x^{\frac{1}{5}} (81)}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.6.1.8

Faktorkan $25 x^{\frac{1}{5}}$ dari $25 x^{\frac{1}{5}} (125 x^{\frac{4}{5}} + 450 x^{\frac{2}{5}} + 375 x^{\frac{3}{5}}) + 25 x^{\frac{1}{5}} (270 x^{\frac{1}{5}})$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{25 x^{\frac{1}{5}} (125 x^{\frac{4}{5}} + 450 x^{\frac{2}{5}} + 375 x^{\frac{3}{5}} + 270 x^{\frac{1}{5}}) + 25 x^{\frac{1}{5}} (81)}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.6.1.9

Faktorkan $25 x^{\frac{1}{5}}$ dari $25 x^{\frac{1}{5}} (125 x^{\frac{4}{5}} + 450 x^{\frac{2}{5}} + 375 x^{\frac{3}{5}} + 270 x^{\frac{1}{5}}) + 25 x^{\frac{1}{5}} (81)$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{25 x^{\frac{1}{5}} (125 x^{\frac{4}{5}} + 450 x^{\frac{2}{5}} + 375 x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} + 81)}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.1.6.2

Susun kembali suku-suku.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{25 x^{\frac{1}{5}} (450 x^{\frac{2}{5}} + 375 x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} + 125 x^{\frac{4}{5}} + 81)}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.2

Faktorkan $25$ dari $25 x^{\frac{1}{5}} (450 x^{\frac{2}{5}} + 375 x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} + 125 x^{\frac{4}{5}} + 81)$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{25 (x^{\frac{1}{5}} (450 x^{\frac{2}{5}} + 375 x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} + 125 x^{\frac{4}{5}} + 81))}{3125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.3

Batalkan faktor persekutuan.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.8.3.1

Faktorkan $25$ dari $3125$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{25 (x^{\frac{1}{5}} (450 x^{\frac{2}{5}} + 375 x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} + 125 x^{\frac{4}{5}} + 81))}{25 \cdot 125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.8.3.2

Batalkan faktor persekutuan.

Langkah 5.2.8.3.3

Tulis kembali pernyataannya.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{x^{\frac{1}{5}} (450 x^{\frac{2}{5}} + 375 x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} + 125 x^{\frac{4}{5}} + 81)}{125} - \frac{3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.9

Gabungkan pembilang dari penyebut persekutuan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{x^{\frac{1}{5}} (450 x^{\frac{2}{5}} + 375 x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} + 125 x^{\frac{4}{5}} + 81) - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.10.1

Terapkan sifat distributif.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{x^{\frac{1}{5}} (450 x^{\frac{2}{5}}) + x^{\frac{1}{5}} (375 x^{\frac{3}{5}}) + x^{\frac{1}{5}} (270 x^{\frac{1}{5}}) + x^{\frac{1}{5}} (125 x^{\frac{4}{5}}) + x^{\frac{1}{5}} \cdot 81 - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.2

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.10.2.1

Tulis kembali menggunakan sifat komutatif dari perkalian.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{1}{5}} x^{\frac{2}{5}} + x^{\frac{1}{5}} (375 x^{\frac{3}{5}}) + x^{\frac{1}{5}} (270 x^{\frac{1}{5}}) + x^{\frac{1}{5}} (125 x^{\frac{4}{5}}) + x^{\frac{1}{5}} \cdot 81 - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.2.2

Tulis kembali menggunakan sifat komutatif dari perkalian.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{1}{5}} x^{\frac{2}{5}} + 375 x^{\frac{1}{5}} x^{\frac{3}{5}} + x^{\frac{1}{5}} (270 x^{\frac{1}{5}}) + x^{\frac{1}{5}} (125 x^{\frac{4}{5}}) + x^{\frac{1}{5}} \cdot 81 - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.2.3

Tulis kembali menggunakan sifat komutatif dari perkalian.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{1}{5}} x^{\frac{2}{5}} + 375 x^{\frac{1}{5}} x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} x^{\frac{1}{5}} + x^{\frac{1}{5}} (125 x^{\frac{4}{5}}) + x^{\frac{1}{5}} \cdot 81 - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.2.4

Tulis kembali menggunakan sifat komutatif dari perkalian.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{1}{5}} x^{\frac{2}{5}} + 375 x^{\frac{1}{5}} x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} x^{\frac{1}{5}} + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + x^{\frac{1}{5}} \cdot 81 - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.2.5

Pindahkan $81$ ke sebelah kiri $x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{1}{5}} x^{\frac{2}{5}} + 375 x^{\frac{1}{5}} x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} x^{\frac{1}{5}} + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.10.3.1

Kalikan $x^{\frac{1}{5}}$ dengan $x^{\frac{2}{5}}$ dengan menambahkan eksponennya.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.10.3.1.1

Pindahkan $x^{\frac{2}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 (x^{\frac{2}{5}} x^{\frac{1}{5}}) + 375 x^{\frac{1}{5}} x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} x^{\frac{1}{5}} + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.1.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{2}{5} + \frac{1}{5}} + 375 x^{\frac{1}{5}} x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} x^{\frac{1}{5}} + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.1.3

Gabungkan pembilang dari penyebut persekutuan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{2 + 1}{5}} + 375 x^{\frac{1}{5}} x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} x^{\frac{1}{5}} + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.1.4

Tambahkan $2$ dan $1$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{1}{5}} x^{\frac{3}{5}} + 270 x^{\frac{1}{5}} x^{\frac{1}{5}} + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.2

Kalikan $x^{\frac{1}{5}}$ dengan $x^{\frac{3}{5}}$ dengan menambahkan eksponennya.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.10.3.2.1

Pindahkan $x^{\frac{3}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 (x^{\frac{3}{5}} x^{\frac{1}{5}}) + 270 x^{\frac{1}{5}} x^{\frac{1}{5}} + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.2.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{3}{5} + \frac{1}{5}} + 270 x^{\frac{1}{5}} x^{\frac{1}{5}} + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.2.3

Gabungkan pembilang dari penyebut persekutuan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{3 + 1}{5}} + 270 x^{\frac{1}{5}} x^{\frac{1}{5}} + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.2.4

Tambahkan $3$ dan $1$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{1}{5}} x^{\frac{1}{5}} + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.3

Kalikan $x^{\frac{1}{5}}$ dengan $x^{\frac{1}{5}}$ dengan menambahkan eksponennya.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.10.3.3.1

Pindahkan $x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 (x^{\frac{1}{5}} x^{\frac{1}{5}}) + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.3.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{1}{5} + \frac{1}{5}} + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.3.3

Gabungkan pembilang dari penyebut persekutuan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{1 + 1}{5}} + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.3.4

Tambahkan $1$ dan $1$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x^{\frac{1}{5}} x^{\frac{4}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.4

Kalikan $x^{\frac{1}{5}}$ dengan $x^{\frac{4}{5}}$ dengan menambahkan eksponennya.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.10.3.4.1

Pindahkan $x^{\frac{4}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 (x^{\frac{4}{5}} x^{\frac{1}{5}}) + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.4.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x^{\frac{4}{5} + \frac{1}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.4.3

Gabungkan pembilang dari penyebut persekutuan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x^{\frac{4 + 1}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.4.4

Tambahkan $4$ dan $1$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x^{\frac{5}{5}} + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.3.4.5

Bagilah $5$ dengan $5$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 \cdot x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (27 + 90 x^{\frac{1}{5}} + 125 x^{\frac{3}{5}} + 150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.4

Terapkan sifat distributif.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} \cdot 27 - 3 x^{\frac{1}{5}} (90 x^{\frac{1}{5}}) - 3 x^{\frac{1}{5}} (125 x^{\frac{3}{5}}) - 3 x^{\frac{1}{5}} (150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.5

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.10.5.1

Kalikan $27$ dengan $- 3$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 3 x^{\frac{1}{5}} (90 x^{\frac{1}{5}}) - 3 x^{\frac{1}{5}} (125 x^{\frac{3}{5}}) - 3 x^{\frac{1}{5}} (150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.5.2

Tulis kembali menggunakan sifat komutatif dari perkalian.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 3 \cdot (90 x^{\frac{1}{5}} x^{\frac{1}{5}}) - 3 x^{\frac{1}{5}} (125 x^{\frac{3}{5}}) - 3 x^{\frac{1}{5}} (150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.5.3

Tulis kembali menggunakan sifat komutatif dari perkalian.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 3 \cdot (90 x^{\frac{1}{5}} x^{\frac{1}{5}}) - 3 \cdot (125 x^{\frac{1}{5}} x^{\frac{3}{5}}) - 3 x^{\frac{1}{5}} (150 x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.5.4

Tulis kembali menggunakan sifat komutatif dari perkalian.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 3 \cdot (90 x^{\frac{1}{5}} x^{\frac{1}{5}}) - 3 \cdot (125 x^{\frac{1}{5}} x^{\frac{3}{5}}) - 3 \cdot (150 x^{\frac{1}{5}} x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.6

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.10.6.1

Kalikan $x^{\frac{1}{5}}$ dengan $x^{\frac{1}{5}}$ dengan menambahkan eksponennya.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.10.6.1.1

Pindahkan $x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 3 \cdot (90 (x^{\frac{1}{5}} x^{\frac{1}{5}})) - 3 \cdot (125 x^{\frac{1}{5}} x^{\frac{3}{5}}) - 3 \cdot (150 x^{\frac{1}{5}} x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.6.1.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 3 \cdot (90 x^{\frac{1}{5} + \frac{1}{5}}) - 3 \cdot (125 x^{\frac{1}{5}} x^{\frac{3}{5}}) - 3 \cdot (150 x^{\frac{1}{5}} x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.6.1.3

Gabungkan pembilang dari penyebut persekutuan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 3 \cdot (90 x^{\frac{1 + 1}{5}}) - 3 \cdot (125 x^{\frac{1}{5}} x^{\frac{3}{5}}) - 3 \cdot (150 x^{\frac{1}{5}} x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.6.1.4

Tambahkan $1$ dan $1$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 3 \cdot (90 x^{\frac{2}{5}}) - 3 \cdot (125 x^{\frac{1}{5}} x^{\frac{3}{5}}) - 3 \cdot (150 x^{\frac{1}{5}} x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.6.2

Kalikan $- 3$ dengan $90$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 270 x^{\frac{2}{5}} - 3 \cdot (125 x^{\frac{1}{5}} x^{\frac{3}{5}}) - 3 \cdot (150 x^{\frac{1}{5}} x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.6.3

Kalikan $x^{\frac{1}{5}}$ dengan $x^{\frac{3}{5}}$ dengan menambahkan eksponennya.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.10.6.3.1

Pindahkan $x^{\frac{3}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 270 x^{\frac{2}{5}} - 3 \cdot (125 (x^{\frac{3}{5}} x^{\frac{1}{5}})) - 3 \cdot (150 x^{\frac{1}{5}} x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.6.3.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 270 x^{\frac{2}{5}} - 3 \cdot (125 x^{\frac{3}{5} + \frac{1}{5}}) - 3 \cdot (150 x^{\frac{1}{5}} x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.6.3.3

Gabungkan pembilang dari penyebut persekutuan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 270 x^{\frac{2}{5}} - 3 \cdot (125 x^{\frac{3 + 1}{5}}) - 3 \cdot (150 x^{\frac{1}{5}} x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.6.3.4

Tambahkan $3$ dan $1$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 270 x^{\frac{2}{5}} - 3 \cdot (125 x^{\frac{4}{5}}) - 3 \cdot (150 x^{\frac{1}{5}} x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.6.4

Kalikan $- 3$ dengan $125$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 270 x^{\frac{2}{5}} - 375 x^{\frac{4}{5}} - 3 \cdot (150 x^{\frac{1}{5}} x^{\frac{2}{5}})}{125}$

Langkah 5.2.10.6.5

Kalikan $x^{\frac{1}{5}}$ dengan $x^{\frac{2}{5}}$ dengan menambahkan eksponennya.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.10.6.5.1

Pindahkan $x^{\frac{2}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 270 x^{\frac{2}{5}} - 375 x^{\frac{4}{5}} - 3 \cdot (150 (x^{\frac{2}{5}} x^{\frac{1}{5}}))}{125}$

Langkah 5.2.10.6.5.2

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 270 x^{\frac{2}{5}} - 375 x^{\frac{4}{5}} - 3 \cdot (150 x^{\frac{2}{5} + \frac{1}{5}})}{125}$

Langkah 5.2.10.6.5.3

Gabungkan pembilang dari penyebut persekutuan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 270 x^{\frac{2}{5}} - 375 x^{\frac{4}{5}} - 3 \cdot (150 x^{\frac{2 + 1}{5}})}{125}$

Langkah 5.2.10.6.5.4

Tambahkan $2$ dan $1$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 270 x^{\frac{2}{5}} - 375 x^{\frac{4}{5}} - 3 \cdot (150 x^{\frac{3}{5}})}{125}$

Langkah 5.2.10.6.6

Kalikan $- 3$ dengan $150$ .

Langkah 5.2.11

Sederhanakan suku-suku.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.11.1

Gabungkan suku balikan dalam $450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 81 x^{\frac{1}{5}} - 81 x^{\frac{1}{5}} - 270 x^{\frac{2}{5}} - 375 x^{\frac{4}{5}} - 450 x^{\frac{3}{5}}$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.11.1.1

Kurangi $81 x^{\frac{1}{5}}$ dengan $81 x^{\frac{1}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x + 0 - 270 x^{\frac{2}{5}} - 375 x^{\frac{4}{5}} - 450 x^{\frac{3}{5}}}{125}$

Langkah 5.2.11.1.2

Tambahkan $450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x$ dan $0$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 270 x^{\frac{2}{5}} + 125 x - 270 x^{\frac{2}{5}} - 375 x^{\frac{4}{5}} - 450 x^{\frac{3}{5}}}{125}$

Langkah 5.2.11.1.3

Kurangi $270 x^{\frac{2}{5}}$ dengan $270 x^{\frac{2}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 125 x + 0 - 375 x^{\frac{4}{5}} - 450 x^{\frac{3}{5}}}{125}$

Langkah 5.2.11.1.4

Tambahkan $450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 125 x$ dan $0$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 375 x^{\frac{4}{5}} + 125 x - 375 x^{\frac{4}{5}} - 450 x^{\frac{3}{5}}}{125}$

Langkah 5.2.11.1.5

Kurangi $375 x^{\frac{4}{5}}$ dengan $375 x^{\frac{4}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 125 x + 0 - 450 x^{\frac{3}{5}}}{125}$

Langkah 5.2.11.1.6

Tambahkan $450 x^{\frac{3}{5}} + 125 x$ dan $0$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{450 x^{\frac{3}{5}} + 125 x - 450 x^{\frac{3}{5}}}{125}$

Langkah 5.2.11.1.7

Kurangi $450 x^{\frac{3}{5}}$ dengan $450 x^{\frac{3}{5}}$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{125 x + 0}{125}$

Langkah 5.2.11.1.8

Tambahkan $125 x$ dan $0$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{125 x}{125}$

Langkah 5.2.11.2

Batalkan faktor persekutuan dari $125$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.11.2.1

Batalkan faktor persekutuan.

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = \frac{125 x}{125}$

Langkah 5.2.11.2.2

Bagilah $x$ dengan $1$ .

$f^{- 1} (5 x^{\frac{1}{5}} + 3) = x$

Langkah 5.3

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

Ketuk untuk lebih banyak langkah...

Langkah 5.3.1

Tulis fungsi hasil komposit.

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

Langkah 5.3.2

Evaluasi $f (- \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125})$ dengan mensubstitusikan nilai (Variabel1) ke dalam (Variabel2).

$f (- \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125}) = 5 {(- \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125})}^{\frac{1}{5}} + 3$

Langkah 5.3.3

Pindahkan $- \frac{243}{3125}$ .

$f (- \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125}) = 5 {(\frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125} - \frac{243}{3125})}^{\frac{1}{5}} + 3$

Langkah 5.3.4

Pindahkan $\frac{81 x}{625}$ .

$f (- \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125}) = 5 {(- \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125} + \frac{81 x}{625} - \frac{243}{3125})}^{\frac{1}{5}} + 3$

Langkah 5.3.5

Pindahkan $- \frac{54 x^{2}}{625}$ .

$f (- \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125}) = 5 {(\frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125} - \frac{54 x^{2}}{625} + \frac{81 x}{625} - \frac{243}{3125})}^{\frac{1}{5}} + 3$

Langkah 5.3.6

Pindahkan $\frac{18 x^{3}}{625}$ .

$f (- \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125}) = 5 {(- \frac{3 x^{4}}{625} + \frac{x^{5}}{3125} + \frac{18 x^{3}}{625} - \frac{54 x^{2}}{625} + \frac{81 x}{625} - \frac{243}{3125})}^{\frac{1}{5}} + 3$

Langkah 5.3.7

Susun kembali $- \frac{3 x^{4}}{625}$ dan $\frac{x^{5}}{3125}$ .

$f (- \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125}) = 5 {(\frac{x^{5}}{3125} - \frac{3 x^{4}}{625} + \frac{18 x^{3}}{625} - \frac{54 x^{2}}{625} + \frac{81 x}{625} - \frac{243}{3125})}^{\frac{1}{5}} + 3$

Langkah 5.4

Karena $f^{- 1} (f (x)) = x$ dan $f (f^{- 1} (x)) = x$ , maka $f^{- 1} (x) = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125}$ merupakan balikan dari $f (x) = 5 x^{\frac{1}{5}} + 3$ .

$f^{- 1} (x) = - \frac{243}{3125} + \frac{81 x}{625} - \frac{54 x^{2}}{625} + \frac{18 x^{3}}{625} - \frac{3 x^{4}}{625} + \frac{x^{5}}{3125}$