1. **State the problem:** Simplify the expression $9 \times 9\sqrt{9} \div 4\sqrt{9}$. 2. **Recall the rules:** The square root of 9 is $\sqrt{9} = 3$. Multiplication and division are performed from left to right. 3. **Substitute the values:** Replace $\sqrt{9}$ with 3 in the expression: $$9 \times 9 \times 3 \div 4 \times 3$$ 4. **Simplify step-by-step:** - Multiply $9 \times 9 = 81$. - Then multiply $81 \times 3 = 243$. - Multiply $4 \times 3 = 12$. - Now divide $243 \div 12$. 5. **Perform the division:** $$\frac{243}{12} = 20.25$$ 6. **Final answer:** The simplified value of the expression is $20.25$.