Aljabar Contoh

${(2 x + \frac{1}{x^{3}})}^{8}$

Langkah 1

Segitiga Pascal dapat ditampilkan sebagai berikut:

$1$

$1 - 1$

$1 - 2 - 1$

$\dots$

$1 - 6 - 15 - 20 - 15 - 6 - 1$

$1 - 7 - 21 - 35 - 35 - 21 - 7 - 1$

$1 - 8 - 28 - 56 - 70 - 56 - 28 - 8 - 1$

Segitiganya dapat digunakan untuk menghitung koefisien dari perluasan ${(a + b)}^{n}$ dengan mengambil pangkat $n$ dan menambahkan $1$ . Koefisien akan sesuai dengan garis $n + 1$ dari segitiga. Untuk ${(2 x + \frac{1}{x^{3}})}^{8}$ $n = 8$ sehingga koefisien dari perluasan akan sesuai dengan garis $9$ .

Langkah 2

Perluasan mengikuti aturan ${(a + b)}^{n} = c_{0} a^{n} b^{0} + c_{1} a^{n - 1} b^{1} + c_{n - 1} a^{1} b^{n - 1} + c_{n} a^{0} b^{n}$ . Nilai-nilai koefisien, dari segitiga, adalah $1 - 8 - 28 - 56 - 70 - 56 - 28 - 8 - 1$ .

$1 a^{8} b^{0} + 8 a^{7} b + 28 a^{6} b^{2} + 56 a^{5} b^{3} + 70 a^{4} b^{4} + 56 a^{3} b^{5} + 28 a^{2} b^{6} + 8 a b^{7} + 1 a^{0} b^{8}$

Langkah 3

Substitusikan nilai-nilai aktual dari $a$ $2 x$ dan $b$ $\frac{1}{x^{3}}$ ke dalam pernyataannya.

$1 {(2 x)}^{8} {(\frac{1}{x^{3}})}^{0} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4

Sederhanakan setiap suku.

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Langkah 4.1

Kalikan ${(2 x)}^{8}$ dengan $1$ .

${(2 x)}^{8} {(\frac{1}{x^{3}})}^{0} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.2

Terapkan kaidah hasil kali ke $2 x$ .

$2^{8} x^{8} {(\frac{1}{x^{3}})}^{0} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.3

Naikkan $2$ menjadi pangkat $8$ .

$256 x^{8} {(\frac{1}{x^{3}})}^{0} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.4

Terapkan kaidah hasil kali ke $\frac{1}{x^{3}}$ .

$256 x^{8} \frac{1^{0}}{{(x^{3})}^{0}} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.5

Apa pun yang dinaikkan ke $0$ adalah $1$ .

$256 x^{8} \frac{1}{{(x^{3})}^{0}} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.6

Sederhanakan penyebutnya.

Ketuk untuk lebih banyak langkah...

Langkah 4.6.1

Kalikan eksponen dalam ${(x^{3})}^{0}$ .

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Langkah 4.6.1.1

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

$256 x^{8} \frac{1}{x^{3 \cdot 0}} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.6.1.2

Kalikan $3$ dengan $0$ .

$256 x^{8} \frac{1}{x^{0}} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.6.2

Apa pun yang dinaikkan ke $0$ adalah $1$ .

$256 x^{8} \frac{1}{1} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.7

Bagilah $1$ dengan $1$ .

$256 x^{8} \cdot 1 + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.8

Kalikan $256$ dengan $1$ .

$256 x^{8} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.9

Terapkan kaidah hasil kali ke $2 x$ .

$256 x^{8} + 8 (2^{7} x^{7}) {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.10

Naikkan $2$ menjadi pangkat $7$ .

$256 x^{8} + 8 (128 x^{7}) {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.11

Kalikan $128$ dengan $8$ .

$256 x^{8} + 1024 x^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.12

Sederhanakan.

$256 x^{8} + 1024 x^{7} \frac{1}{x^{3}} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.13

Batalkan faktor persekutuan dari $x^{3}$ .

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Langkah 4.13.1

Faktorkan $x^{3}$ dari $1024 x^{7}$ .

$256 x^{8} + x^{3} (1024 x^{4}) \frac{1}{x^{3}} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.13.2

Batalkan faktor persekutuan.

Langkah 4.13.3

Tulis kembali pernyataannya.

$256 x^{8} + 1024 x^{4} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.14

Terapkan kaidah hasil kali ke $2 x$ .

$256 x^{8} + 1024 x^{4} + 28 (2^{6} x^{6}) {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.15

Naikkan $2$ menjadi pangkat $6$ .

$256 x^{8} + 1024 x^{4} + 28 (64 x^{6}) {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.16

Kalikan $64$ dengan $28$ .

$256 x^{8} + 1024 x^{4} + 1792 x^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.17

Terapkan kaidah hasil kali ke $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 x^{6} \frac{1^{2}}{{(x^{3})}^{2}} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.18

Satu dipangkat berapa pun sama dengan satu.

$256 x^{8} + 1024 x^{4} + 1792 x^{6} \frac{1}{{(x^{3})}^{2}} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.19

Kalikan eksponen dalam ${(x^{3})}^{2}$ .

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Langkah 4.19.1

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

$256 x^{8} + 1024 x^{4} + 1792 x^{6} \frac{1}{x^{3 \cdot 2}} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.19.2

Kalikan $3$ dengan $2$ .

$256 x^{8} + 1024 x^{4} + 1792 x^{6} \frac{1}{x^{6}} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.20

Batalkan faktor persekutuan dari $x^{6}$ .

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Langkah 4.20.1

Faktorkan $x^{6}$ dari $1792 x^{6}$ .

$256 x^{8} + 1024 x^{4} + x^{6} \cdot 1792 \frac{1}{x^{6}} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.20.2

Batalkan faktor persekutuan.

Langkah 4.20.3

Tulis kembali pernyataannya.

$256 x^{8} + 1024 x^{4} + 1792 + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.21

Terapkan kaidah hasil kali ke $2 x$ .

$256 x^{8} + 1024 x^{4} + 1792 + 56 (2^{5} x^{5}) {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.22

Naikkan $2$ menjadi pangkat $5$ .

$256 x^{8} + 1024 x^{4} + 1792 + 56 (32 x^{5}) {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.23

Kalikan $32$ dengan $56$ .

$256 x^{8} + 1024 x^{4} + 1792 + 1792 x^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.24

Terapkan kaidah hasil kali ke $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + 1792 x^{5} \frac{1^{3}}{{(x^{3})}^{3}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.25

Satu dipangkat berapa pun sama dengan satu.

$256 x^{8} + 1024 x^{4} + 1792 + 1792 x^{5} \frac{1}{{(x^{3})}^{3}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.26

Kalikan eksponen dalam ${(x^{3})}^{3}$ .

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Langkah 4.26.1

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

$256 x^{8} + 1024 x^{4} + 1792 + 1792 x^{5} \frac{1}{x^{3 \cdot 3}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.26.2

Kalikan $3$ dengan $3$ .

$256 x^{8} + 1024 x^{4} + 1792 + 1792 x^{5} \frac{1}{x^{9}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.27

Batalkan faktor persekutuan dari $x^{5}$ .

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Langkah 4.27.1

Faktorkan $x^{5}$ dari $1792 x^{5}$ .

$256 x^{8} + 1024 x^{4} + 1792 + x^{5} \cdot 1792 \frac{1}{x^{9}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.27.2

Faktorkan $x^{5}$ dari $x^{9}$ .

$256 x^{8} + 1024 x^{4} + 1792 + x^{5} \cdot 1792 \frac{1}{x^{5} x^{4}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.27.3

Batalkan faktor persekutuan.

Langkah 4.27.4

Tulis kembali pernyataannya.

$256 x^{8} + 1024 x^{4} + 1792 + 1792 \frac{1}{x^{4}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.28

Gabungkan $1792$ dan $\frac{1}{x^{4}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.29

Terapkan kaidah hasil kali ke $2 x$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 70 (2^{4} x^{4}) {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.30

Naikkan $2$ menjadi pangkat $4$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 70 (16 x^{4}) {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.31

Kalikan $16$ dengan $70$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 1120 x^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.32

Terapkan kaidah hasil kali ke $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 1120 x^{4} \frac{1^{4}}{{(x^{3})}^{4}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.33

Satu dipangkat berapa pun sama dengan satu.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 1120 x^{4} \frac{1}{{(x^{3})}^{4}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.34

Kalikan eksponen dalam ${(x^{3})}^{4}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.34.1

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

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 1120 x^{4} \frac{1}{x^{3 \cdot 4}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.34.2

Kalikan $3$ dengan $4$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 1120 x^{4} \frac{1}{x^{12}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.35

Batalkan faktor persekutuan dari $x^{4}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.35.1

Faktorkan $x^{4}$ dari $1120 x^{4}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + x^{4} \cdot 1120 \frac{1}{x^{12}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.35.2

Faktorkan $x^{4}$ dari $x^{12}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + x^{4} \cdot 1120 \frac{1}{x^{4} x^{8}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.35.3

Batalkan faktor persekutuan.

Langkah 4.35.4

Tulis kembali pernyataannya.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 1120 \frac{1}{x^{8}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.36

Gabungkan $1120$ dan $\frac{1}{x^{8}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.37

Terapkan kaidah hasil kali ke $2 x$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 56 (2^{3} x^{3}) {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.38

Naikkan $2$ menjadi pangkat $3$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 56 (8 x^{3}) {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.39

Kalikan $8$ dengan $56$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 448 x^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.40

Terapkan kaidah hasil kali ke $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 448 x^{3} \frac{1^{5}}{{(x^{3})}^{5}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.41

Satu dipangkat berapa pun sama dengan satu.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 448 x^{3} \frac{1}{{(x^{3})}^{5}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.42

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

Ketuk untuk lebih banyak langkah...

Langkah 4.42.1

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

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 448 x^{3} \frac{1}{x^{3 \cdot 5}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.42.2

Kalikan $3$ dengan $5$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 448 x^{3} \frac{1}{x^{15}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.43

Batalkan faktor persekutuan dari $x^{3}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.43.1

Faktorkan $x^{3}$ dari $448 x^{3}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + x^{3} \cdot 448 \frac{1}{x^{15}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.43.2

Faktorkan $x^{3}$ dari $x^{15}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + x^{3} \cdot 448 \frac{1}{x^{3} x^{12}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.43.3

Batalkan faktor persekutuan.

Langkah 4.43.4

Tulis kembali pernyataannya.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 448 \frac{1}{x^{12}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.44

Gabungkan $448$ dan $\frac{1}{x^{12}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.45

Terapkan kaidah hasil kali ke $2 x$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 28 (2^{2} x^{2}) {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.46

Naikkan $2$ menjadi pangkat $2$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 28 (4 x^{2}) {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.47

Kalikan $4$ dengan $28$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 112 x^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.48

Terapkan kaidah hasil kali ke $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 112 x^{2} \frac{1^{6}}{{(x^{3})}^{6}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.49

Satu dipangkat berapa pun sama dengan satu.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 112 x^{2} \frac{1}{{(x^{3})}^{6}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.50

Kalikan eksponen dalam ${(x^{3})}^{6}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.50.1

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

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 112 x^{2} \frac{1}{x^{3 \cdot 6}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.50.2

Kalikan $3$ dengan $6$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 112 x^{2} \frac{1}{x^{18}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.51

Batalkan faktor persekutuan dari $x^{2}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.51.1

Faktorkan $x^{2}$ dari $112 x^{2}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + x^{2} \cdot 112 \frac{1}{x^{18}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.51.2

Faktorkan $x^{2}$ dari $x^{18}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + x^{2} \cdot 112 \frac{1}{x^{2} x^{16}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.51.3

Batalkan faktor persekutuan.

Langkah 4.51.4

Tulis kembali pernyataannya.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 112 \frac{1}{x^{16}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.52

Gabungkan $112$ dan $\frac{1}{x^{16}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.53

Sederhanakan.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 8 (2 x) {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.54

Kalikan $2$ dengan $8$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 16 x {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.55

Terapkan kaidah hasil kali ke $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 16 x \frac{1^{7}}{{(x^{3})}^{7}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.56

Satu dipangkat berapa pun sama dengan satu.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 16 x \frac{1}{{(x^{3})}^{7}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.57

Kalikan eksponen dalam ${(x^{3})}^{7}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.57.1

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

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 16 x \frac{1}{x^{3 \cdot 7}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.57.2

Kalikan $3$ dengan $7$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 16 x \frac{1}{x^{21}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.58

Batalkan faktor persekutuan dari $x$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.58.1

Faktorkan $x$ dari $16 x$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + x \cdot 16 \frac{1}{x^{21}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.58.2

Faktorkan $x$ dari $x^{21}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + x \cdot 16 \frac{1}{x \cdot x^{20}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.58.3

Batalkan faktor persekutuan.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + x \cdot 16 \frac{1}{x \cdot x^{20}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.58.4

Tulis kembali pernyataannya.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 16 \frac{1}{x^{20}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.59

Gabungkan $16$ dan $\frac{1}{x^{20}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.60

Kalikan ${(2 x)}^{0}$ dengan $1$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.61

Terapkan kaidah hasil kali ke $2 x$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + 2^{0} x^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.62

Apa pun yang dinaikkan ke $0$ adalah $1$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + 1 x^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.63

Kalikan $x^{0}$ dengan $1$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + x^{0} {(\frac{1}{x^{3}})}^{8}$

Langkah 4.64

Apa pun yang dinaikkan ke $0$ adalah $1$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + 1 {(\frac{1}{x^{3}})}^{8}$

Langkah 4.65

Kalikan ${(\frac{1}{x^{3}})}^{8}$ dengan $1$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + {(\frac{1}{x^{3}})}^{8}$

Langkah 4.66

Terapkan kaidah hasil kali ke $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + \frac{1^{8}}{{(x^{3})}^{8}}$

Langkah 4.67

Satu dipangkat berapa pun sama dengan satu.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + \frac{1}{{(x^{3})}^{8}}$

Langkah 4.68

Kalikan eksponen dalam ${(x^{3})}^{8}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.68.1

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

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + \frac{1}{x^{3 \cdot 8}}$

Langkah 4.68.2

Kalikan $3$ dengan $8$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + \frac{1}{x^{24}}$