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

Using the properties of radicals, the expression, $\dfrac{\sqrt[3]{a^6}}{\sqrt[3]{b^9}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[3]{a^6}}{\sqrt[3]{b^9}} \\\\= \dfrac{\sqrt[3]{(a^2)^3}}{\sqrt[3]{(b^3)^3}} \\\\= \dfrac{a^2}{b^3} .\end{array} Note that the variable/s is/are assumed to be positive. Hence, $\text{ Choice A .}$