From Förberedande kurs i matematik 1

We can write \displaystyle 9=3\centerdot 3=3^{2} and then the power rules give

\displaystyle 9^{\frac{3}{2}}=\left( 3^{2} \right)^{\frac{3}{2}}=3^{2\centerdot \frac{3}{2}}=3^{3}=3\centerdot 3\centerdot 3=27