Answer
$\sqrt[3]{x}$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
\sqrt[9]{x^3}
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^{3/9}
\\\\=
x^{1/3}
\\\\=
\sqrt[3]{x^1}
\\\\=
\sqrt[3]{x}
.\end{array}