Simplify the Expression: 5^9 ÷ 5^9 in Fraction Form

To solve this problem, we apply the Power of a Quotient Rule for exponents. This rule is applicable when both the numerator and the denominator of a fraction have the same base. The rule states:

$\frac{a^m}{a^n} = a^{m-n}$

For our problem, the expression is:

$\frac{5^9}{5^9}$

In this expression, the base $a$ is $5$, $m$ is $9$, and $n$$$ is also $9$. We apply the rule as follows:

$\frac{5^9}{5^9} = 5^{9-9}$

Calculating the exponent:

$9 - 9 = 0$

So the expression becomes:

$5^0$

Any number raised to the power of 0 is 1, but in this context, we are simply reducing the original expression to its simplest form. Therefore, $5^0$ is the correct answer.

The solution to the question is: $5^0$