Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set - Page 433: 73

$2a^2\sqrt[4]{2}$

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}