To simplify the expression $\frac{x^3}{x^2}$, you can apply the exponent subtraction rule, which yields $x^{3-2} = x^1$, or simply $x$.

When simplifying expressions that involve exponents, you can utilize the important rule that states:

This rule indicates that when dividing two powers with the same base, you subtract the exponent of the denominator from the exponent of the numerator. In our example, the base is $x$, the exponent in the numerator is $3$, and the exponent in the denominator is $2$. Therefore, we perform the subtraction $3 - 2$, which results in:

Let’s break this down further for clarity. The expression $\frac{x^3}{x^2}$ can be understood as having $x$ multiplied by itself three times in the numerator, and $x$ multiplied by itself two times in the denominator:

When you divide these quantities, you can cancel out two $x$ factors from both the numerator and the denominator, leaving you with just one $x$ in the numerator. This visual representation reinforces the result that:

Grasping this rule is invaluable, as it allows you to simplify more complex expressions and solve equations with greater ease. Remember that this rule applies only when the bases are the same. Practicing this with various numbers and variables will enhance your confidence in simplifying expressions that involve exponents.