+140 Assuming that\(p \neq 0\) and\(q \neq 0\) , simplify \(\dfrac{(pq^3)^3(4p^2q)^2}{(2pq^2)^3}\) plz include a step by step explanation
+9519 You should know that
\(p^a\cdot p^b = p^{a + b} \qquad (1)\\ \dfrac{p^a}{p^b} = p^{a - b}\qquad (2)\\ \left(p^a\right)^b = p^{ab}\qquad (3)\\ (pq)^a = p^a q^a\qquad (4)\)
Using these three formulae,
\(\quad \dfrac{\left(pq^3\right)^3\cdot \left(4p^2q\right)^2}{\left(2pq^2\right)^3}\\ \stackrel{(4)}{=} \dfrac{p^3 \left(q^3\right)^3\cdot 4^2 \cdot \left(p^2\right)^2\cdot q^2}{2^3 \cdot p^3 \cdot \left(q^2\right)^3}\\ \stackrel{(3)}{=} \dfrac{p^3q^9\cdot16\cdot p^4\cdot q^2}{8p^3q^6}\\ = 2\cdot \dfrac{p^3\cdot p^4}{p^3} \cdot \dfrac{q^9 \cdot q^2}{q^6}\)
Can you do the rest with identities (1) and (2)?
