## Intermediate Algebra (12th Edition)

$\dfrac{\sqrt[3]{18}}{3}$
$\bf{\text{Solution Outline:}}$ To rationalize the given radical expression, $\sqrt[3]{\dfrac{2}{3}} ,$ multiply the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index. $\bf{\text{Solution Details:}}$ Multiplying the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{2}{3}\cdot\dfrac{3^2}{3^2}} \\\\= \sqrt[3]{\dfrac{2(3^2)}{3^3}} \\\\= \sqrt[3]{\dfrac{2(9)}{3^3}} \\\\= \sqrt[3]{\dfrac{18}{3^3}} .\end{array} Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{\sqrt[3]{18}}{\sqrt[3]{3^3}} \\\\= \dfrac{\sqrt[3]{18}}{3} .\end{array}