Answer
$\frac{2}{3}$.
Work Step by Step
If $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers with $b\ne0$, then according to the quotient for radicals: $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n] a}{\sqrt[n] b}$.
$\sqrt[3] 8$ and $\sqrt[3] {27}$ are real numbers with $27\ne0$, then according to the quotient for radicals: $\sqrt[3]{\frac{8}{27}}=\frac{\sqrt[3] 8}{\sqrt[3] {27}}=\frac{2}{3}$.
