Assuming that p and q are nonzero, simplify \( \dfrac{(pq^3)^3(4p^2q)^2}{(2pq^2)^3}\)
\(\frac{(pq^3)^3(4p^2q)^2}{(2pq^2)^3} = \frac{(p^3q^9)(16p^4q^2)}{8p^3q^6} = \frac{16p^7q^{11}}{8p^3q^6}\)
\(\boxed{2p^4q^5}\)