Question: If $\frac{36^x}{3^{11}}$ is an integer, what is the smallest possible integer value of $x$? I'd like to know the approach to this problem.

Answer: 
**Hint:** $36^x=9^x \times 4^x=3^{2x}\times 4^x$.
Hint: $$\frac{(36)^x}{3^{11}}=\frac{3^{2x}(4)^{x}}{3^{11}}=3^{2x-11}(4)^{x}.$$