SOLUTION: Assuming that p \neq 0 and q \neq 0, simplify \dfrac{(pq^2)^2 (4pq^2)^3 (2p^2 q^3)^2}{(p^2 q^3)^8 (pq^8)^2 (p^4 q^5)^6}.

Question 1209067: Assuming that p \neq 0 and q \neq 0, simplify \dfrac{(pq^2)^2 (4pq^2)^3 (2p^2 q^3)^2}{(p^2 q^3)^8 (pq^8)^2 (p^4 q^5)^6}.
Answer by yurtman(42) (Show Source): You can put this solution on YOUR website!
Let's simplify the expression step-by-step:
**Step 1: Apply the power rule to each term:**
$$\frac{p^2q^4 \cdot 64p^3q^6 \cdot 4p^4q^6}{p^{16}q^{24} \cdot p^2q^{16} \cdot p^{24}q^{30}}$$
**Step 2: Combine like terms in the numerator and denominator:**
$$\frac{256p^9q^{16}}{p^{42}q^{70}}$$
**Step 3: Apply the quotient rule:**
$$256p^{9-42}q^{16-70}$$
**Step 4: Simplify the exponents:**
$$256p^{-33}q^{-54}$$
**Step 5: Use the negative exponent rule:**
$$\frac{256}{p^{33}q^{54}}$$
Therefore, the simplified expression is:
$$\frac{256}{p^{33}q^{54}}$$

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