Answer
$\dfrac{x^{6}}{4y^{2}}$
Work Step by Step
Using the laws of exponents, the given expression, $
(2x^{-3}y)^{-2}
,$ simplifies to
\begin{array}{l}\require{cancel}
2^{-2}x^{-3(-2)}y^{-2}
\\\\=
2^{-2}x^{6}y^{-2}
\\\\=
\dfrac{x^{6}}{2^{2}y^{2}}
\\\\=
\dfrac{x^{6}}{4y^{2}}
.\end{array}
