Answer
$8$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{1}{16} \right)^{-3/4}
,$ is equivalent to
\begin{array}{l}\require{cancel}
16^{3/4}
.\end{array}
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $
16^{3/4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[4]{16^3}
\\\\=
\left( \sqrt[4]{16} \right) ^3
\\\\=
\left( \sqrt[4]{(2)^4} \right) ^3
\\\\=
\left( 2 \right) ^3
\\\\=
8
.\end{array}
