Answer
$\dfrac{1}{16x^{12}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{4x^5}{2x^2} \right)^{-4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\left( (4\div2)x^{5-2} \right)^{-4}
\\\\=
\left( 2x^{3} \right)^{-4}
\\\\=
2^{1(-4)}x^{3(-4)}
\\\\=
2^{-4}x^{-12}
\\\\=
\dfrac{1}{2^{4}x^{12}}
\\\\=
\dfrac{1}{16x^{12}}
.\end{array}