Simplify the Exponential Expression: 9^x ÷ 9^y

We start with the expression: $\frac{9^x}{9^y}$.
We need to simplify this expression using the Power of a Quotient Rule for exponents, which states that $\frac{a^m}{a^n} = a^{m-n}$. Here, the base $a$ must be the same in both the numerator and the denominator, and we subtract the exponent of the denominator from the exponent of the numerator.

Applying this rule to our expression, we identify $a = 9$, $m = x$, and $n = y$. So we have:

• $a = 9$
• $m = x$
• $n = y$

Using the Power of a Quotient Rule, we therefore rewrite the expression as:

$a^{m-n} = 9^{x-y}$

Hence, the simplified expression of $\frac{9^x}{9^y}$ is $9^{x-y}$.

The solution to the question is: $9^{x-y}$