Simplify (x^4)^-3*2x^4

${(x^{4})}^{- 3} \cdot 2 x^{4}$

Step 1

Rewrite using the commutative property of multiplication.

$2 {(x^{4})}^{- 3} x^{4}$

Step 2

Multiply the exponents in ${(x^{4})}^{- 3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 x^{4 \cdot - 3} x^{4}$

Multiply $4$ by $- 3$ .

$2 x^{- 12} x^{4}$

Step 3

Multiply $x^{- 12}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$2 (x^{4} x^{- 12})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 x^{4 - 12}$

Subtract $12$ from $4$ .

$2 x^{- 8}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$2 \frac{1}{x^{8}}$

Step 5

Combine $2$ and $\frac{1}{x^{8}}$ .

$\frac{2}{x^{8}}$