#### Answer

$\dfrac{\sqrt[4]{96a^{10}b^{3}}}{\sqrt[4]{3a^{2}b^{3}}}=2a^{2}\sqrt[4]{2}$

#### Work Step by Step

$\dfrac{\sqrt[4]{96a^{10}b^{3}}}{\sqrt[4]{3a^{2}b^{3}}}$
Rewrite the expression as $\sqrt[4]{\dfrac{96a^{10}b^{3}}{3a^{2}b^{3}}}$ and evaluate the division inside the root:
$\dfrac{\sqrt[4]{96a^{10}b^{3}}}{\sqrt[4]{3a^{2}b^{3}}}=\sqrt[4]{\dfrac{96a^{10}b^{3}}{3a^{2}b^{3}}}=\sqrt[4]{32a^{10-2}}=\sqrt[4]{32a^{8}}=...$
Rewrite the expression inside the root as $16\cdot2\cdot a^{8}$ and simplify:
$...=\sqrt[4]{16\cdot2\cdot a^{8}}=2a^{2}\sqrt[4]{2}$