Answer
$\dfrac{1}{27}$
Work Step by Step
Using $a^{-x}=\dfrac{1}{a^x}$ and $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
(81)^{-3/4}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{1}{81^{3/4}}
\\\\=
\dfrac{1}{(\sqrt[4]{81})^{3}}
\\\\=
\dfrac{1}{\left( \sqrt[4]{(3)^4} \right)^{3}}
\\\\=
\dfrac{1}{3^{3}}
\\\\=
\dfrac{1}{27}
.\end{array}
