1. The problem is to simplify the expression $9^{\frac{3}{2}}$. 2. Recall the rule for fractional exponents: $a^{\frac{m}{n}} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m$. 3. Here, $9^{\frac{3}{2}} = (\sqrt{9})^3$ because the denominator 2 means square root. 4. Calculate $\sqrt{9} = 3$. 5. Now raise 3 to the power of 3: $3^3 = 27$. 6. Therefore, $9^{\frac{3}{2}} = 27$. Final answer: 27