Answer
$4a^2|b|\sqrt[4]{2a}$
Work Step by Step
Using the properties of radicals, the expression $
\dfrac{2\sqrt[4]{32a^{8}b^{6}}}{\sqrt[4]{a^{-1}b^2}}
$ simplifies to
\begin{array}{l}
2\sqrt[4]{\dfrac{32a^{8}b^{6}}{a^{-1}b^2}}
\\\\=
2\sqrt[4]{32a^{8-(-1)}b^{6-2}}
\\\\=
2\sqrt[4]{32a^{9}b^{4}}
\\\\=
2\sqrt[4]{16a^{8}b^{4}\cdot2a}
\\\\=
2\cdot2a^2|b|\sqrt[4]{2a}
\\\\=
4a^2|b|\sqrt[4]{2a}
.\end{array}
