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

$\dfrac{\sqrt[3]{5a^2b}}{ab}$
Rationalizing the denominator of the given expression, $\sqrt[3]{\dfrac{5}{ab^2}} ,$ we find: \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{5}{ab^2}\cdot\dfrac{a^2b}{a^2b}} \\\\= \sqrt[3]{\dfrac{5a^2b}{a^3b^3}} \\\\= \dfrac{\sqrt[3]{5a^2b}}{\sqrt[3]{a^3b^3}} \\\\= \dfrac{\sqrt[3]{5a^2b}}{\sqrt[3]{(ab)^3}} \\\\= \dfrac{\sqrt[3]{5a^2b}}{ab} .\end{array} * Note that it is assumed that all variables represent positive numbers.