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