Answer
$\frac{\sqrt[3] 4}{2}$
Work Step by Step
First, we simplify the given expression,
$\sqrt[3] \frac{1}{2}=\frac{\sqrt[3] 1}{\sqrt[3] 2}=\frac{1}{\sqrt[3] 2}$
Next, we rationalize its denominator by multiplying the fraction by a term that will remove the rational exponent in the denominator,
$\frac{1}{\sqrt[3] 2}\times\frac{\sqrt[3] 4}{\sqrt[3] 4}$
=$\frac{1\times\sqrt[3] 4}{\sqrt[3] 2\times\sqrt[3] 4}$
=$\frac{\sqrt[3] 4}{\sqrt[3] {2\times4}}$
=$\frac{\sqrt[3] 4}{\sqrt[3] {8}}$
=$\frac{\sqrt[3] 4}{2}$
