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

$\dfrac{y\sqrt[4]{45x^3y^2}}{3x}$
Rationalizing the denominator of the given expression, $\dfrac{\sqrt[4]{5y^6}}{\sqrt[4]{9x}} ,$ we find: \begin{array}{l}\require{cancel} \dfrac{\sqrt[4]{5y^6}}{\sqrt[4]{9x}}\cdot\dfrac{\sqrt[3]{9x^3}}{\sqrt[3]{9x^3}} \\\\= \dfrac{\sqrt[4]{45x^3y^6}}{\sqrt[4]{81x^4}} \\\\= \dfrac{\sqrt[4]{y^4\cdot45x^3y^2}}{\sqrt[4]{81x^4}} \\\\= \dfrac{\sqrt[4]{(y)^4\cdot45x^3y^2}}{\sqrt[4]{(3x)^4}} \\\\= \dfrac{y\sqrt[4]{45x^3y^2}}{3x} .\end{array} * Note that it is assumed that all variables represent positive numbers.