#### Answer

$\dfrac{\sqrt[4]{28a^2}}{4ab}$

#### Work Step by Step

Rationalizing the denominator of the given expression, $
\sqrt[4]{\dfrac{7}{64a^2b^4}}
,$ we find:
\begin{array}{l}\require{cancel}
\sqrt[4]{\dfrac{7}{64a^2b^4}\cdot\dfrac{4a^2}{4a^2}}
\\\\=
\sqrt[4]{\dfrac{28a^2}{256a^4b^4}}
\\\\=
\dfrac{\sqrt[4]{28a^2}}{\sqrt[4]{256a^4b^4}}
\\\\=
\dfrac{\sqrt[4]{28a^2}}{\sqrt[4]{(4ab)^4}}
\\\\=
\dfrac{\sqrt[4]{28a^2}}{4ab}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.