Question

Which expression is equivalent to (4p^-4q)^-2/10pq^-3? Assume p and q do not equal 0. A. 25p^10/4q^8 B. 2q/5p^5 C. p^7q/160 D. 125p^11q/2

Answer 1

The equivalent expression to 
(4p^-4q)^-2/10pq^-3
=(4^-2p^(-4*-2)q^-2)/(10pq^-3)
=(4^-2p^8q^-2)/(10pq^-3)
=[p^8q^-2/16]/[10pq^-3]
=p^7q/160

Answer: C]p^7q/160

Answer 2

Answer: C. $=\frac{p^7q}{160} .$

Step-by-step explanation: Given expression $\frac{(4p^{-4}q)^{-2}}{10pq^{-3}}$.

Applying exponents of exponent rule $(ab)^c = a^cb^c$ and

negative power rule $(a)^{n} = \frac{1}{a^n}$.

$(4p^{-4}q)^{-2} = 4^{-2}p^{-4\times(-2)q^{-2}} = \frac{1\times p^8}{4^2q^2}$

= $\frac{(4p^{-4}q)^{-2}}{10pq^{-3}}= \frac{1\times p^8q^3}{10\times 4^2pq^2}$

$= \frac{ p^8q^3}{160pq^2}$

Apply quotient rule of exponents $\frac{a^m}{a^n} = a^{m-n}$.

$\frac{ p^8q^3}{160pq^2}= \frac{p^{8-1}q^{3-2}}{160}$

$=\frac{p^7q}{160} .$

Therefore, correct option is C. $=\frac{p^7q}{160} .$