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

$\sqrt[10]{xy^{3}}$
Using the same indices for the radicals, the given expression, $\dfrac{\sqrt[5]{x^3y^4}}{\sqrt[]{xy}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[5(2)]{x^{3(2)}y^{4(2)}}}{\sqrt[2(5)]{x^{1(5)}y^{1(5)}}} \\\\= \dfrac{\sqrt[10]{x^{6}y^{8}}}{\sqrt[10]{x^{5}y^{5}}} \\\\= \sqrt[10]{\dfrac{x^{6}y^{8}}{x^{5}y^{5}}} \\\\= \sqrt[10]{x^{6-5}y^{8-5}} \\\\= \sqrt[10]{x^{1}y^{3}} \\\\= \sqrt[10]{xy^{3}} \end{array} * Note that it is assumed that all variables represent positive numbers.