Answer: C. [tex]=\frac{p^7q}{160} .[/tex]
Step-by-step explanation: Given expression [tex]\frac{(4p^{-4}q)^{-2}}{10pq^{-3}}[/tex].
Applying exponents of exponent rule [tex](ab)^c = a^cb^c[/tex] and
negative power rule [tex](a)^{n} = \frac{1}{a^n}[/tex].
[tex](4p^{-4}q)^{-2} = 4^{-2}p^{-4\times(-2)q^{-2}} = \frac{1\times p^8}{4^2q^2}[/tex]
= [tex]\frac{(4p^{-4}q)^{-2}}{10pq^{-3}}= \frac{1\times p^8q^3}{10\times 4^2pq^2}[/tex]
[tex]= \frac{ p^8q^3}{160pq^2}[/tex]
Apply quotient rule of exponents [tex]\frac{a^m}{a^n} = a^{m-n}[/tex].
[tex]\frac{ p^8q^3}{160pq^2}= \frac{p^{8-1}q^{3-2}}{160}[/tex]
[tex]=\frac{p^7q}{160} .[/tex]
Therefore, correct option is C. [tex]=\frac{p^7q}{160} .[/tex]
