Answer
$ \dfrac{5\sqrt[3] 4}{2}$
Work Step by Step
Rationalize the denominator by multiplying $\sqrt[3]{4}$ to both the numerator and the denominator:
$\dfrac{5}{\sqrt[3] 2}=\dfrac{5}{\sqrt[3] 2}\cdot \dfrac{\sqrt[3] 4}{\sqrt[3] 4}$
Use the rule $\sqrt[n]{a} \cdot \sqrt[n]{b}=\sqrt[n]{a\cdot b}$ then simplify:
$= \dfrac{5\sqrt[3] 4}{\sqrt[3] {2\cdot 4}}$
$= \dfrac{5\sqrt[3] 4}{\sqrt[3] {8}}$
$= \dfrac{5\sqrt[3] 4}{\sqrt[3] {2^3}}$
$= \dfrac{5\sqrt[3] 4}{2}$
Hence, the correct answer is $ \frac{5\sqrt[3] 4}{2}$.
