1. **State the problem:** Simplify the expression $\frac{2}{2x^2}$.\n\n2. **Write the expression:** $\frac{2}{2x^2}$.\n\n3. **Simplify the fraction by canceling common factors:** Both numerator and denominator have a factor of 2.\n$$\frac{\cancel{2}}{\cancel{2}x^2} = \frac{1}{x^2}$$\n\n4. **Final simplified expression:** $\frac{1}{x^2}$.\n\nThis means dividing 2 by $2x^2$ simplifies to $\frac{1}{x^2}$, assuming $x \neq 0$ to avoid division by zero.