Answer
$8$
Work Step by Step
Using $x^{-a}=\dfrac{1}{x^a}$ and $\dfrac{1}{x^{-a}}=x^a,$ the given expression, $
\dfrac{2^{-3}}{8^{-2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{8^{2}}{2^{3}}
\\\\=
\dfrac{64}{8}
\\\\=
8
.\end{array}