1. The problem is to determine if the expression $\frac{1}{2}x^2$ is correct or not. 2. This expression represents a term where $x$ is squared and then multiplied by $\frac{1}{2}$. 3. The expression $\frac{1}{2}x^2$ is mathematically correct and commonly used, for example in physics for kinetic energy $KE = \frac{1}{2}mv^2$. 4. If you meant $\frac{1}{2x^2}$, that would be different and written as $\frac{1}{2x^2}$, which is not the same as $\frac{1}{2}x^2$. 5. So, $\frac{1}{2}x^2$ is not wrong; it is a valid algebraic expression. 6. To clarify, $\frac{1}{2}x^2$ means $\left(\frac{1}{2}\right) \times x^2$. 7. Therefore, the expression $\frac{1}{2}x^2$ is correct as it stands.