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