## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$2\sqrt[3]{a^{2}b^{}}$
Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression, $\dfrac{\sqrt[3]{96a^4b^2}}{\sqrt[3]{12a^2b}} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{\sqrt[3]{96a^4b^2}}{\sqrt[3]{12a^2b}} \\\\= \sqrt[3]{\dfrac{96a^4b^2}{12a^2b}} \\\\= \sqrt[3]{8a^{4-2}b^{2-1}} \\\\= \sqrt[3]{8a^{2}b^{}} .\end{array} Extracting the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[3]{8a^{2}b^{}} \\\\= \sqrt[3]{8\cdot a^{2}b^{}} \\\\= \sqrt[3]{(2)^3\cdot a^{2}b^{}} \\\\= 2\sqrt[3]{a^{2}b^{}} .\end{array} Note that all variables are assumed to be positive.