#### Answer

$27\sqrt[4]{x^3}$

#### Work Step by Step

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