1. **State the problem:** Simplify the expression $p^3 q^2 \times p^2 q$. 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 to each variable:** - For $p$: $$p^3 \times p^2 = p^{3+2} = p^5$$ - For $q$: $$q^2 \times q = q^{2+1} = q^3$$ 4. **Combine the results:** $$p^5 q^3$$ 5. **Final answer:** The simplified expression is $p^5 q^3$.