The problem asks us to evaluate $9^{\frac{5}{2}}$.

1. Problem Description

The problem asks us to evaluate $9^{\frac{5}{2}}$.

2. Solution Steps

We can rewrite the expression as follows:

$9^{\frac{5}{2}} = (9^{\frac{1}{2}})^5$

Since $9^{\frac{1}{2}} = \sqrt{9} = 3$, we have

$(9^{\frac{1}{2}})^5 = 3^5$.

Now we calculate $3^5$:

$3^1 = 3$

$3^2 = 9$

$3^3 = 27$

$3^4 = 81$

$3^5 = 3^4 \times 3 = 81 \times 3 = 243$.

Therefore, $9^{\frac{5}{2}} = 243$.

3. Final Answer

243