Question

Which expression is equivalent to (1/4ab)^-2? Assume a is not equal to 0,b is not equal to 0

a. -1/16a^2b^2
b. a^2b^2/4
c. -16a^2b^2
d. 16a^2b^2

Answer 1

The answer would be D. 

Answer 2

d.
`16a^2b^2`

Explanation:

Given expression,

`((1)/(4ab))^(-2)`

`=((4ab)^(-1))^(-2)`
`\because (1)/(a^m)=a^(-m)`

`=(4ab)^(-1* -2)`
`\because (a^m)^n=a^(mn)`

`=(4ab)^2`

`=(4)^2(a)^2(b)^2`
`\because (ab)^m=a^mb^m`

`=16a^2b^2`

Hence, option d is correct.