Simplify (2x^2)^-4

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

Step 1

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

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

Step 2

Simplify the denominator.

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

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

Raise $2$ to the power of $4$ .

$\frac{1}{16 {(x^{2})}^{4}}$

Multiply the exponents in ${(x^{2})}^{4}$ .

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

$\frac{1}{16 x^{2 \cdot 4}}$

Multiply $2$ by $4$ .

$\frac{1}{16 x^{8}}$