1. **State the problem:** Simplify the expression $3^{11} \times 9^{15}$. 2. **Rewrite the bases:** Note that $9 = 3^2$, so we can rewrite $9^{15}$ as $(3^2)^{15}$. 3. **Apply the power of a power rule:** $(3^2)^{15} = 3^{2 \times 15} = 3^{30}$. 4. **Rewrite the expression:** Now the expression is $3^{11} \times 3^{30}$. 5. **Apply the product of powers rule:** When multiplying powers with the same base, add the exponents: $3^{11} \times 3^{30} = 3^{11 + 30} = 3^{41}$. 6. **Final answer:** The simplified form is $$3^{41}$$.