Answer
$\dfrac{\sqrt[5]{9y^4}}{2xy}$
Work Step by Step
Rationalizing the denominator of the given expression, $
\sqrt[5]{\dfrac{9}{32x^5y}}
,$ we find:
\begin{array}{l}\require{cancel}
\sqrt[5]{\dfrac{9}{32x^5y}\cdot\dfrac{y^4}{y^4}}
\\\\=
\sqrt[5]{\dfrac{9y^4}{32x^5y^5}}
\\\\=
\dfrac{\sqrt[5]{9y^4}}{\sqrt[5]{32x^5y^5}}
\\\\=
\dfrac{\sqrt[5]{9y^4}}{\sqrt[5]{(2xy)^5}}
\\\\=
\dfrac{\sqrt[5]{9y^4}}{2xy}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.