1. **State the problem:** Simplify the expression $ (x^2)^2 $. 2. **Recall the power of a power rule:** When raising a power to another power, multiply the exponents: $$ (a^m)^n = a^{m \times n} $$ 3. **Apply the rule:** Here, $a = x$, $m = 2$, and $n = 2$, so $$ (x^2)^2 = x^{2 \times 2} $$ 4. **Multiply the exponents:** $$ x^{2 \times 2} = x^4 $$ 5. **Final answer:** $$ (x^2)^2 = x^4 $$