Question

How do you simplify `((a^-2)^2)^-3`?

Answer 1

See a solution process below:

Explanation:

First, simplify the term within the outer parenthesis by using this rule of exponents:

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

`((a^color(red)(-2))^color(blue)(2))^-3 = (a^(color(red)(-2) xx color(blue)(2)))^-3 => (a^-4)^-3`

Use this same rule to simplify the remaining expression:

`(a^color(red)(-4))^color(blue)(-3) = a^(color(red)(-4) xx color(blue)(-3)) = a^12`