Answer
$\frac{25x^{6}}{y^{4}}$
Work Step by Step
We know that $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}}=a^{n}$ (as long as a is a nonzero real number and n is an integer).
Therefore, $(5x^{3}y^{-2})^{2}=5^{2}\times(x^{3})^{2}\times(y^{-2})^{2}=25\times x^{3\times2}\times y^{-2\times2}=25\times x^{6}\times y^{-4}=25\times x^{6}\times \frac{1}{y^{4}}=\frac{25x^{6}}{y^{4}}$.