2*2

To solve the expression \[ \frac{\sqrt{16a^b \cdot \sqrt[3]{4b^3}}}{\sqrt{a^5b^3}} \] given \( a = 9 \) and \( b = 11 \), follow these steps: 1. **Substitute the values into the expression:** \[ \frac{\sqrt{16 \cdot 9^{11} \cdot \sqrt[3]{4 \cdot 11^3}}}{\sqrt{9^5 \cdot 11^3}} \] 2. **Simplify each part:** - \( 16 = 2^4 \) - \( \sqrt{16} = 4 \) 3. **Compute powers:** - Calculate \( 9^{11} \) and \( 9^5 \). 4. **Evaluate the cube root and square roots:** - Calculate \( \sqrt[3]{4 \cdot 11^3} \). - Simplify \( \sqrt{a^5b^3} = \sqrt{9^5 \cdot 11^3} \). 5. **Simplify overall expression:** Combine the results to find the simplified value. Proceed with these calculations to get the desired result.