Answer
$\displaystyle \frac{x^{4}}{y^{2}}$
Work Step by Step
Apply rule $\quad(ab)^{n}=a^{n}b^{n}$
$(x^{2}y^{-1})^{2}=(x^{2})^{2}\cdot(y^{-1})^{2}\quad$.
Apply rule $\quad (a^{m})^{n}=a^{mn}$
$=x^{4}y^{-2} \quad$.
Apply rule $\displaystyle \quad a^{-n}=\frac{1}{a^{n}}$
$=\displaystyle x^4 \cdot \frac{1}{y^{2}}\\
=\displaystyle \frac{x^{4}}{y^{2}}$