#### Answer

$2a^{2}b^{6}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\dfrac{\sqrt[5]{64a^{11}b^{28}}}{\sqrt[5]{2ab^{-2}}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[5]{\dfrac{64a^{11}b^{28}}{2ab^{-2}}}
\\\\=
\sqrt[5]{32a^{11-1}b^{28-(-2)}}
\\\\=
\sqrt[5]{32a^{10}b^{30}}
\\\\=
\sqrt[5]{(2a^{2}b^{6})^5}
\\\\=
2a^{2}b^{6}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.