1. **State the problem:** Simplify the expression $(2p^2q)(2pq^2)$. 2. **Recall the multiplication rule for exponents:** When multiplying like bases, add the exponents: $a^m \cdot a^n = a^{m+n}$. 3. **Multiply the coefficients:** $2 \times 2 = 4$. 4. **Multiply the variables:** - For $p$: $p^2 \times p^1 = p^{2+1} = p^3$. - For $q$: $q^1 \times q^2 = q^{1+2} = q^3$. 5. **Combine all parts:** $$ (2p^2q)(2pq^2) = 4p^3q^3 $$ 6. **Final answer:** $4p^3q^3$