#### Answer

Choice E

#### Work Step by Step

Multiplying both the numerator and denominator by $
b
,$ the given expression, $
\sqrt[5]{\dfrac{a^6}{b^4}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[5]{\dfrac{a^6}{b^4}}
\\\\=
\sqrt[5]{\dfrac{a^6}{b^4}\dfrac{b}{b}}
\\\\=
\sqrt[5]{\dfrac{a^6b}{b^4\cdot b}}
.\end{array}
Hence, $\text{
Choice E
.}$