#### Answer

$a^5b^{5}$

#### Work Step by Step

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