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

Answer: C.
`=(p^7q)/(160) .`

Step-by-step explanation: Given expression
`((4p^(-4)q)^(-2))/(10pq^(-3))`.

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

negative power rule
`(a)^(n) = (1)/(a^n)`.

`(4p^(-4)q)^(-2) = 4^(-2)p^{-4*(-2)q^(-2)} = (1* p^8)/(4^2q^2)`

=
`((4p^(-4)q)^(-2))/(10pq^(-3))= (1* p^8q^3)/(10* 4^2pq^2)`

`= ( p^8q^3)/(160pq^2)`

Apply quotient rule of exponents
`(a^m)/(a^n) = a^(m-n)`.

`( p^8q^3)/(160pq^2)= (p^(8-1)q^(3-2))/(160)`

`=(p^7q)/(160) .`

Therefore, correct option is C.
`=(p^7q)/(160) .`

Answer 2

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