#### Answer

$\sqrt[15]{2a}$

#### Work Step by Step

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
\sqrt[5]{\sqrt[3]{2a}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\left( \sqrt[3]{2a} \right)^{\frac{1}{5}}
\\\\=
\left( (2a)^{\frac{1}{3}} \right)^{\frac{1}{5}}
\\\\=
\left( 2a \right)^{\frac{1}{3}\cdot\frac{1}{5}}
\\\\=
\left( 2a \right)^{\frac{1}{15}}
\\\\=
\sqrt[15]{(2a)^1}
\\\\=
\sqrt[15]{2a}
.\end{array}