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

$\dfrac{2a}{bc^2}$
Using the properties of radicals, the given expression, $\sqrt[4]{\dfrac{32a^4}{2b^4c^8}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[4]{\dfrac{16a^4}{b^4c^8}} \\\\= \dfrac{\sqrt[4]{16a^4}}{\sqrt[4]{b^4c^8}} \\\\= \dfrac{\sqrt[4]{(2a)^4}}{\sqrt[4]{(bc^2)^4}} \\\\= \dfrac{2a}{bc^2} \end{array} * Note that it is assumed that all variables represent positive numbers.