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

$(x-y)^{4}$
Using the properties of radicals, the given expression, $\sqrt[3]{(x-y)^2}\sqrt[3]{(x-y)^{10}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[3]{(x-y)^2(x-y)^{10}} \\\\= \sqrt[3]{(x-y)^{2+10}} \\\\= \sqrt[3]{(x-y)^{12}} \\\\= \sqrt[3]{\left[ (x-y)^{4} \right]^3} \\\\= (x-y)^{4} \end{array} * Note that it is assumed that no radicands were formed by raising negative numbers to even powers.