Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers.
-$\left(4 \mathrm{p}^{3} \mathrm{q}^{6}\right)^{-2}\left(16 \mathrm{p}^{4} \mathrm{q}^{2}\right)^{2}$

A) $\frac{16 p^{2}}{q^{8}}$

B) $\frac{16 q^{2}}{p^{-8}}$

C) $\frac{p^{2}}{16 q^{-8}}$

D) $\frac{16 p^{2}}{q^{-8}}$

Question

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers.
-$\left(4 \mathrm{p}^{3} \mathrm{q}^{6}\right)^{-2}\left(16 \mathrm{p}^{4} \mathrm{q}^{2}\right)^{2}$

A) $\frac{16 p^{2}}{q^{8}}$

B) $\frac{16 q^{2}}{p^{-8}}$

C) $\frac{p^{2}}{16 q^{-8}}$

D) $\frac{16 p^{2}}{q^{-8}}$

Quizplus · Accepted Answer

First, apply the power of a power rule: $(a^m)^n = a^{mn}$. For the first term, $(4p^3q^6)^{-2} = 4^{-2}p^{-6}q^{-12}$. For the second term, $(16p^4q^2)^2 = 16^2p^8q^4$. Simplifying, we get $4^{-2} = \frac{1}{16}$ and $16^2 = 256$. Multiplying the terms together: $\frac{1}{16} \cdot 256 \cdot p^{-6+8} \cdot q^{-12+4} = 16p^2q^{-8}$. To ensure all exponents are positive, and since there's no $q$ in the numerator, the correct answer is $\frac{16p^2}{q^8}$.

Simplify Write the Answer with Only Positive Exponents (4p3q6)−2(16p4q2)2\left(4 \mathrm{p}^{3} \mathrm{q}^{6}\right)^{-2}\left(16 \mathrm{p}^{4} \mathrm{q}^{2}\right)^{2}(4p3q6)−2(16p4q2)2

Simplify Write the Answer with Only Positive Exponents $\left(4 \mathrm{p}^{3} \mathrm{q}^{6}\right)^{-2}\left(16 \mathrm{p}^{4} \mathrm{q}^{2}\right)^{2}$