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

$\sqrt[6]{(7-y)^{5}}$
Using the same indices for the radicals, the given expression, $\dfrac{\sqrt[]{(7-y)^3}}{\sqrt[3]{(7-y)^2}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[2(3)]{(7-y)^{3(3)}}}{\sqrt[3(2)]{(7-y)^{2(2)}}} \\\\= \dfrac{\sqrt[6]{(7-y)^{9}}}{\sqrt[6]{(7-y)^{4}}} \\\\= \sqrt[6]{\dfrac{(7-y)^{9}}{(7-y)^{4}}} \\\\= \sqrt[6]{(7-y)^{9-4}} \\\\= \sqrt[6]{(7-y)^{5}} \end{array} * Note that it is assumed that all variables represent positive numbers.