From Förberedande kurs i matematik 1

The number \displaystyle 9 can be written as \displaystyle 9=3\centerdot 3=3^{2}

and hence the denominator in the expression is equal to

\displaystyle 9^{2}=\left( 3^{2} \right)^{2}=3^{2\centerdot 2}=3^{4}

The whole quotient becomes

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