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

$\sqrt[12]{a^{5}}$
Using the same indices for the radicals, the given expression, $\dfrac{\sqrt[3]{a^2}}{\sqrt[4]{a}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[3(4)]{a^{2(4)}}}{\sqrt[4(3)]{a^{1(3)}}} \\\\= \dfrac{\sqrt[12]{a^{8}}}{\sqrt[12]{a^{3}}} \\\\= \sqrt[12]{\dfrac{a^{8}}{a^{3}}} \\\\= \sqrt[12]{a^{8-3}} \\\\= \sqrt[12]{a^{5}} \end{array} * Note that it is assumed that all variables represent positive numbers.