Question

Simplify the expression (StartFraction 1 Over 4 a b EndFraction) Superscript negative 2. Assume a not-equals 0, b not-equals 0.

Answer 1

16 a²b² is option D on e2020

Explanation:

100% on test

Answer 2

The simplest form of the expression is 16 a²b²

Explanation:

* Lets explain how to solve the problem

- To simplify any fraction with exponent you must put it with positive

exponent

- Ex: the fraction
`((2)/(3))^(-1)` not in the simplest form

because it has negative exponent

- To change the negative exponent to positive exponent reciprocal the

fraction,
`((3)/(2))^(1)` and this is the simplest form of the fraction

* Now lets solve the problem

∵ The expression is
`((1)/(4ab))^(-2)`, where a and b ≠ 0

- At first reciprocal the fraction

∴
`((1)/(4ab))^(-2)=((4ab)/(1))^(2)`

- Then solve the power

∵ 4² = 16

∵ (ab)² = a²b²

∴ (4ab)² = 16 a²b²

* The simplest form of the expression is 16 a²b²