Question

Simplify the expression (1/4ab)^-2. Assume a ≠ 0, b ≠ 0

Answer 1

`( (1)/(4ab) )^(-2) = (4ab)^2 = 16a^2b^2`

Answer 2

The expression
`((1)/(4ab))^(-2)` is
`16a^2b^2`

Explanation:

Given : the expression
`((1)/(4ab))^(-2)`

We have to simplify the given expression
`((1)/(4ab))^(-2)`

Consider the given expression
`((1)/(4ab))^(-2)`

Apply exponent rule
`\left((a)/(b)\right)^(-c)=\left(\left((a)/(b)\right)^(-1)\right)^c=\left((b)/(a)\right)^c`

We have,

`=\left((4ab)/(1)\right)^2=\left(4ab\right)^2`

Apply exponent rule ,
`\left(a\cdot \:b\right)^n=a^nb^n`

`=4^2a^2b^2`

Simplify, we get,

`=16a^2b^2`

Thus, The expression
`((1)/(4ab))^(-2)` is
`16a^2b^2`