Simplify the Expression: x^7 ÷ x^2 Using Exponent Rules

To solve the expression $\frac{x^7}{x^2}$, we need to apply the power of a quotient rule for exponents. This rule states that $\frac{a^m}{a^n} = a^{m-n}$, where $a$ is a nonzero number, and $m$ and $n$ are integers. This rule allows us to subtract the exponent in the denominator from the exponent in the numerator, given that the bases are the same.

Here's a step-by-step breakdown of applying the formula:

• Identify the base $x$ which is common in both numerator and denominator.
• Look at the exponents: the numerator has an exponent of 7 and the denominator has an exponent of 2.
• According to the power of a quotient rule, subtract the exponent in the denominator from the exponent in the numerator: $7 - 2$.
• Perform the subtraction: $7 - 2 = 5$.
• The resulting exponent of $x$ is 5.

Therefore, $\frac{x^7}{x^2}$ simplifies to $x^5$.

The solution to the question is: x^5