Simplify the Exponential Expression: 9^15 ÷ 9^10

To solve the expression $\frac{9^{15}}{9^{10}}$, we will use the Power of a Quotient rule for exponents, which states that $\frac{a^m}{a^n} = a^{m-n}$. This rule applies when both the numerator and the denominator have the same base.

In our problem, both the numerator and the denominator have the base 9, hence we can apply the rule:

• Identify the exponents: The exponent in the numerator is 15, and the exponent in the denominator is 10.
• Apply the Power of a Quotient rule by subtracting the exponent of the denominator from the exponent of the numerator:
  $9^{15-10}$
• Calculate the result of the subtraction:
  $15 - 10 = 5$
• Thus, the simplified form of the expression is:
  $9^5$

The solution to the question is: $9^5$