Simplify (-2x^2)^-2

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

Step 1

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

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

Step 2

Simplify the denominator.

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

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

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

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

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

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

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

Multiply $2$ by $2$ .

$\frac{1}{4 x^{4}}$