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

$2a^{}b^{3}\sqrt[4]{5a}$
Using the properties of radicals, the given expression, $\sqrt[4]{20a^3b^7}\sqrt[4]{4a^2b^5} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[4]{20a^3b^7(4a^2b^5)} \\\\= \sqrt[4]{80a^{3+2}b^{7+5}} \\\\= \sqrt[4]{80a^{5}b^{12}} \\\\= \sqrt[4]{16a^{4}b^{12}\cdot5a} \\\\= \sqrt[4]{(2a^{}b^{3})^4\cdot5a} \\\\= 2a^{}b^{3}\sqrt[4]{5a} \end{array} * Note that it is assumed that no radicands were formed by raising negative numbers to even powers.