How do you simplify (4a ^ { - 4} b ^ { - 4} ) ^ { 2}(4a4b4)2?

1 Answer
Apr 12, 2017

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)a=a1 and (x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))(xa)b=xa×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)) =(4a4b4)2=(41a4b4)2=41×2a4×2b4×2=

4^2a^-8b^-8 = 16a^-8b^-842a8b8=16a8b8

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

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

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))16a8b8=16a8b8=16a8b8