Question

How do you simplify `(ab)^-2`?

Answer 1

See the entire simplification process below:

Explanation:

First, remove the negative exponent by using this rule for exponents:

`x^color(red)(a) = 1/x^color(red)(-a)`

`(ab)^color(red)(-2) = 1/(ab)^color(red)(- -2) = 1/(ab)^2`

This may be enough simplification depending on what has been requested. However, if you want to remove the terms from parenthesis you can use these two rules for exponents to further simplify:

`a = a^color(red)(1)` and `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`1/(ab)^2 = 1/(a^color(red)(1)b^color(red)(1))^color(blue)(2) = 1/(a^(color(red)(1) xx color(blue)(2))b^(color(red)(1) xx color(blue)(2))) = 1/(a^2b^2)`