1. The problem is to simplify the expression $\frac{9^9}{9^2}$.\n\n2. We use the rule of exponents that states $\frac{a^m}{a^n} = a^{m-n}$ when the bases are the same.\n\n3. Applying this rule, we get $\frac{9^9}{9^2} = 9^{9-2}$.\n\n4. Simplify the exponent: $9 - 2 = 7$.\n\n5. Therefore, the expression simplifies to $9^7$.\n\n6. The final answer is $9^7$.