Simplify Powers: Finding 25^9 ÷ 25^2 Using Exponent Rules

To solve the expression $\frac{25^9}{25^2}$$$, we will use the Power of a Quotient Rule for Exponents. According to this rule, when dividing like bases, we subtract the exponents.

• $a^m \div a^n = a^{m-n}$

In the given expression, the base $25$ is the same for both the numerator and the denominator. Therefore, we can apply the rule as follows:

• Identify the exponents: $m = 9$ and $n = 2$.

• Subtract the exponents: $9 - 2 = 7$.

• Write the result as a single power of the base: $25^7$.

Thus, the expression $\frac{25^9}{25^2}$ simplifies to $25^7$.

The solution to the question is: 25^7