Answer
$\sqrt[4]{3x}$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
\sqrt[8]{(3x)^2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
(3x)^{2/8}
\\\\=
(3x)^{1/4}
\\\\=
\sqrt[4]{(3x)^1}
\\\\=
\sqrt[4]{3x}
.\end{array}