Question

How do you simplify `(4a ^ { - 4} b ^ { - 4} ) ^ { 2}`?

Answer 1

See the entire solution process below:

Explanation:

First, use these rules of exponents to eliminate the eliminate the outer exponent:

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

`(4a^-4b^-4)^2 = (4^color(red)(1)a^color(red)(-4)b^color(red)(-4))^color(blue)(2) = 4^(color(red)(1) xx color(blue)(2))a^(color(red)(-4) xx color(blue)(2))b^(color(red)(-4) xx color(blue)(2)) =`

`4^2a^-8b^-8 = 16a^-8b^-8`

Now, use this rule of exponents to eliminate the negative exponents:

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

#16a^color(red)(-8)b^color(red)(-8) = 16/(a^color(red)(- -8)b^color(red)(- -8)) = 16/(a^color(red)(8)b^color(red)(8))#