Answer
$\sqrt[5]{3a^4}$
Work Step by Step
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
(3a^4)^{1/5}
\\\\=
\sqrt[5]{3a^4}
.\end{array}