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

$\dfrac{x^4}{\sqrt[3]{2}\sqrt[7]{y^2}}$
Using the laws of exponents, the given expression, $2^{-1/3}x^4y^{-2/7} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{x^4}{2^{1/3}y^{2/7}} .\end{array} Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $\dfrac{x^4}{2^{1/3}y^{2/7}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{x^4}{\sqrt[3]{2^1}\sqrt[7]{y^2}} \\\\= \dfrac{x^4}{\sqrt[3]{2}\sqrt[7]{y^2}} .\end{array}