Simplify the expression $\frac{x^3 x^2}{2x^2}$.

1. Problem Description

Simplify the expression $\frac{x^3 x^2}{2x^2}$.

2. Solution Steps

First, simplify the numerator using the rule $x^a x^b = x^{a+b}$:

$x^3 x^2 = x^{3+2} = x^5$

Now, the expression becomes:

$\frac{x^5}{2x^2}$

Next, simplify the fraction using the rule $\frac{x^a}{x^b} = x^{a-b}$:

$\frac{x^5}{2x^2} = \frac{1}{2} \frac{x^5}{x^2} = \frac{1}{2} x^{5-2} = \frac{1}{2} x^3$

3. Final Answer

$\frac{x^3}{2}$