Answer
$\dfrac{y^{9}}{x^{6}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{x^2}{y^3} \right)^{-3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x^{2(-3)}}{y^{3(-3)}}
\\\\=
\dfrac{x^{-6}}{y^{-9}}
\\\\=
\dfrac{y^{9}}{x^{6}}
.\end{array}