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.