Simplify (-5^-2x^3)^-1

${(- 5^{- 2} x^{3})}^{- 1}$

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

${(- \frac{1}{5^{2}} x^{3})}^{- 1}$

Raise $5$ to the power of $2$ .

${(- \frac{1}{25} x^{3})}^{- 1}$

Combine $x^{3}$ and $\frac{1}{25}$ .

${(- \frac{x^{3}}{25})}^{- 1}$

Change the sign of the exponent by rewriting the base as its reciprocal.

$- \frac{25}{x^{3}}$