Answer
$\dfrac{y^{8}}{x^{12}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{x^3}{y^2} \right)^{-4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x^{3(-4)}}{y^{2(-4)}}
\\\\=
\dfrac{x^{-12}}{y^{-8}}
\\\\=
\dfrac{y^{8}}{x^{12}}
.\end{array}