Answer
$\dfrac{1}{4p^{4}}$
Work Step by Step
Using laws of exponents, then,
\begin{array}{l}
\left( \dfrac{8p^6}{4p^4} \right)^{-2}
\\\\=
\left( 2p^{6-4} \right)^{-2}
\\\\=
\left( 2p^{2} \right)^{-2}
\\\\=
2^{-2}p^{2(-2)}
\\\\=
2^{-2}p^{-4}
\\\\=
\dfrac{1}{2^{2}p^{4}}
\\\\=
\dfrac{1}{4p^{4}}
.\end{array}
