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

1 Answer
May 8, 2017

Answer:

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#