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

$\dfrac{2\sqrt[4]{a^3}\sqrt[3]{c^2}}{\sqrt{b}}$
Using the laws of exponents, the given expression, $2a^{3/4}b^{-1/2}c^{2/3} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{2a^{3/4}c^{2/3}}{b^{1/2}} .\end{array} Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $\dfrac{2a^{3/4}c^{2/3}}{b^{1/2}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{2\sqrt[4]{a^3}\sqrt[3]{c^2}}{\sqrt{b}} .\end{array}