From Förberedande kurs i matematik 1

The number 9 can be written as \displaystyle 9=3\cdot 3=3^{2} and hence the denominator in the expression is equal to

\displaystyle 9^{2} = (3^{2})^{2} = 3^{2\cdot 2} = 3^{4}\,.

The whole quotient becomes

\displaystyle \frac{3}{9^{2}}=\frac{3^{1}}{3^{4}}=3^{1-4}=3^{^{-3}}.