Simplify (2x^-4)^3

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

Step 1

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

${(2 \frac{1}{x^{4}})}^{3}$

Step 2

Combine $2$ and $\frac{1}{x^{4}}$ .

${(\frac{2}{x^{4}})}^{3}$

Step 3

Simplify the expression.

Apply the product rule to $\frac{2}{x^{4}}$ .

$\frac{2^{3}}{{(x^{4})}^{3}}$

Raise $2$ to the power of $3$ .

$\frac{8}{{(x^{4})}^{3}}$

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

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

$\frac{8}{x^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{8}{x^{12}}$