Simplify (m/(n^2))^-2

${(\frac{m}{n^{2}})}^{- 2}$

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

${(\frac{n^{2}}{m})}^{2}$

Apply the product rule to $\frac{n^{2}}{m}$ .

$\frac{{(n^{2})}^{2}}{m^{2}}$

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

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

$\frac{n^{2 \cdot 2}}{m^{2}}$

Multiply $2$ by $2$ .

$\frac{n^{4}}{m^{2}}$