1. The problem is to evaluate $(-2)^2$. 2. The formula for exponentiation is $a^n = a \times a \times \cdots \times a$ ($n$ times). 3. Here, $a = -2$ and $n = 2$, so we multiply $-2$ by itself twice. 4. Calculate: $$(-2)^2 = (-2) \times (-2)$$ 5. Multiplying two negative numbers results in a positive number, so: $$(-2) \times (-2) = 4$$ 6. Therefore, the final answer is $4$.