Answer
$2a^2\sqrt[4]{2}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
\dfrac{\sqrt[4]{96a^{10}b^{3}}}{\sqrt[4]{3a^2b^3}}
\\\\=
\sqrt[4]{\dfrac{96a^{10}b^{3}}{3a^2b^3}}
\\\\=
\sqrt[4]{32a^{10-2}b^{3-3}}
\\\\=
\sqrt[4]{32a^{8}}
\\\\=
\sqrt[4]{16a^{8}\cdot2}
\\\\=
2a^2\sqrt[4]{2}
.\end{array}