Answer
$\displaystyle \frac{y^{3}}{x^{3}}$
Work Step by Step
Apply rule $\quad(ab)^{n}=a^{n}b^{n}$
$(x^{-1}y)^{3}=(x^{-1})^{3}\cdot(y^{3})\quad$
Apply rule $\quad (a^{m})^{n}=a^{mn}$
$=x^{-3}y^{3} \quad$.
Apply rule $\displaystyle \quad a^{-n}=\frac{1}{a^{n}}$
$=\displaystyle \frac{1}{x^{3}} \cdot y^3
\\=\displaystyle \frac{y^{3}}{x^{3}}$