\( \operatorname{Simpliyy}: \frac{\sqrt{9} \times 3^{4} \times 2^{5}}{\sqrt{16} \times(\sqrt{9})^{3}} \) \( = \) \( = \)

1. Replace the square roots with their numerical values: \[ \sqrt{9} = 3 \quad \text{and} \quad \sqrt{16} = 4. \] The expression becomes: \[ \frac{3 \times 3^4 \times 2^5}{4 \times 3^3}. \] 2. Combine the powers of \(3\) in the numerator: \[ 3 \times 3^4 = 3^{1+4} = 3^5. \] Now the expression is: \[ \frac{3^5 \times 2^5}{4 \times 3^3}. \] 3. Simplify the fraction by canceling the common factor \(3^3\): \[ \frac{3^5}{3^3} = 3^{5-3} = 3^2. \] Thus, the expression becomes: \[ \frac{3^2 \times 2^5}{4}. \] 4. Evaluate \(3^2\) and \(2^5\): \[ 3^2 = 9 \quad \text{and} \quad 2^5 = 32. \] So, the expression simplifies to: \[ \frac{9 \times 32}{4}. \] 5. Perform the multiplication and division: \[ 9 \times 32 = 288 \quad \text{and} \quad \frac{288}{4} = 72. \] The simplified result is: \[ 72. \]