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