Answer
$4$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{1}{8} \right)^{-2/3}
,$ is equivalent to
\begin{array}{l}\require{cancel}
8^{2/3}
.\end{array}
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $
8^{2/3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3]{8^2}
\\\\=
\left( \sqrt[3]{8} \right) ^2
\\\\=
\left( 2 \right) ^2
\\\\=
4
.\end{array}
