#### Answer

$a^{6}b^{12}$

#### Work Step by Step

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
\left( \sqrt[5]{a^2b^4} \right)^{15}
,$ is equivalent to
\begin{array}{l}\require{cancel}
(a^2b^4)^{15/5}
\\\\=
(a^2b^4)^{3}
\\\\=
a^{2(3)}b^{4(3)}
\\\\=
a^{6}b^{12}
.\end{array}