#### Answer

$\dfrac{3x}{y^2z}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\sqrt[4]{\dfrac{81x^4}{y^8z^4}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[4]{81x^4}}{\sqrt[4]{y^8z^4}}
\\\\=
\dfrac{\sqrt[4]{(3x)^4}}{\sqrt[4]{(y^2z)^4}}
\\\\=
\dfrac{3x}{y^2z}
\end{array}
* Note that it is assumed that all variables represent positive numbers.