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

$\dfrac{5\sqrt[3]{2}}{2}$
$\bf{\text{Solution Outline:}}$ To rationalize the denominator of the given expression, $\dfrac{5}{\sqrt[3]{4}} ,$ multiply by an expression equal to $1$ which will make the denominator a perfect power of the index. $\bf{\text{Solution Details:}}$ Multiplying the given expression by an expression equal to $1$ which will make the denominator a perfect power of the index and then simplifying the radical result to \begin{array}{l}\require{cancel} \dfrac{5}{\sqrt[3]{4}}\cdot\dfrac{\sqrt[3]{2}}{\sqrt[3]{2}} \\\\= \dfrac{5\sqrt[3]{2}}{\sqrt[3]{8}} \\\\= \dfrac{5\sqrt[3]{2}}{\sqrt[3]{(2)^3}} \\\\= \dfrac{5\sqrt[3]{2}}{2} .\end{array}