1. **State the problem:** Simplify the expression $x^2 \times x^2$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$ 3. **Apply the rule:** Here, the base is $x$, and the exponents are both 2, so: $$x^2 \times x^2 = x^{2+2}$$ 4. **Simplify the exponent:** $$x^{2+2} = x^4$$ 5. **Final answer:** The simplified form of $x^2 \times x^2$ is $x^4$.