Answer
1/9
Work Step by Step
We know the following rule: $$(\sqrt[n] x)=x^{\frac{1}{n}}$$
Using this as well as the rules of exponents learned in a past chapter (and listed on page 330, if review is necessary), we find:
$$\frac{1}{27^{\frac{2}{3}}} \\ =\frac{1}{9}$$
