Answer
$\frac{1}{\sqrt[3] (x+2)}$
Work Step by Step
We are told on page 419 that $a^{\frac{m}{n}}=\sqrt[n] (a^{m})$ (where m and n are positive integers greater than 1 with $\frac{m}{n}$ in simplest form and $\sqrt[n] a$ is a real number).
Therefore, $(x+2)^{-\frac{1}{3}}=\frac{1}{(x+2)^{\frac{1}{3}}}=\frac{1}{\sqrt[3] (x+2)}$