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

$2a^{2}b^{6}$
Using the properties of radicals, the given expression, $\dfrac{\sqrt[5]{64a^{11}b^{28}}}{\sqrt[5]{2ab^{-2}}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[5]{\dfrac{64a^{11}b^{28}}{2ab^{-2}}} \\\\= \sqrt[5]{32a^{11-1}b^{28-(-2)}} \\\\= \sqrt[5]{32a^{10}b^{30}} \\\\= \sqrt[5]{(2a^{2}b^{6})^5} \\\\= 2a^{2}b^{6} .\end{array} * Note that it is assumed that all variables represent positive numbers.