1. **Problem Statement:** Simplify the expression $\frac{p^{2}q^{3}}{4} \times 8 \div 2p^{2}q$. 2. **Recall the rules:** - When multiplying fractions, multiply numerators and denominators. - Division by a term is the same as multiplying by its reciprocal. - When dividing expressions with the same base, subtract exponents: $a^{m} \div a^{n} = a^{m-n}$. 3. **Rewrite the expression:** $$\frac{p^{2}q^{3}}{4} \times 8 \div 2p^{2}q = \frac{p^{2}q^{3}}{4} \times 8 \times \frac{1}{2p^{2}q}$$ 4. **Multiply numerators and denominators:** $$= \frac{p^{2}q^{3} \times 8 \times 1}{4 \times 2p^{2}q} = \frac{8p^{2}q^{3}}{8p^{2}q}$$ 5. **Cancel common factors:** $$= \frac{\cancel{8}p^{2}q^{3}}{\cancel{8}p^{2}q}$$ 6. **Simplify powers:** $$= \frac{p^{2}q^{3}}{p^{2}q} = p^{2-2}q^{3-1} = p^{0}q^{2}$$ 7. **Recall that $p^{0} = 1$:** $$= 1 \times q^{2} = q^{2}$$ **Final answer:** $q^{2}$