## Algebra: A Combined Approach (4th Edition)

$\dfrac{3}{7\sqrt[3]{3}}$
$\bf{\text{Solution Outline:}}$ To rationalize the numerator of the given expression, $\dfrac{\sqrt[3]{9}}{7} ,$ multiply by an expression equal to $1$ which will make the numerator a perfect power of the index. Then extract the root of the factor that is a perfect power of the index. $\bf{\text{Solution Details:}}$ Multiplying the given expression by an expression equal to $1$ which will make the numerator a perfect power of the index results to \begin{array}{l}\require{cancel} \dfrac{\sqrt[3]{9}}{7}\cdot\dfrac{\sqrt[3]{3}}{\sqrt[3]{3}} \\\\= \dfrac{\sqrt[3]{27}}{7\sqrt[3]{3}} \\\\= \dfrac{\sqrt[3]{(3)^3}}{7\sqrt[3]{3}} \\\\= \dfrac{3}{7\sqrt[3]{3}} .\end{array}