#### Answer

$\sqrt[4]{(2x)^3}$

#### Work Step by Step

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
\left( \sqrt[8]{2x} \right)^6
,$ is equivalent to
\begin{array}{l}\require{cancel}
(2x)^{6/8}
\\\\=
(2x)^{3/4}
\\\\=
\sqrt[4]{(2x)^3}
.\end{array}