Answer
$\frac{1}{\sqrt (x+2y)}$
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, $(x+2y)^{-\frac{1}{2}}=\frac{1}{(x+2y)^{\frac{1}{2}}}=\frac{1}{\sqrt (x+2y)}$
