Answer
$2\sqrt[3]{2}$
Work Step by Step
Apply the rule$\quad \displaystyle \frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}$
$\displaystyle \frac{\sqrt[3]{32}}{\sqrt[3]{2}}=\sqrt[3]{\frac{32}{2}}$
$=\sqrt[3]{16}$
... recognize a power of 2, $16=2^{4}=2^{3}\cdot 2^{1}$
$=\sqrt[3]{2^{3}\cdot 2^{1}} \quad$... use the rule: $\sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}$
$=\sqrt[3]{2^{3}}\cdot\sqrt[3]{2}\quad $... for odd-indexed roots, $\sqrt[n]{a^{n}}=a$
= $2\sqrt[3]{2}$
