How do you simplify [(4r^2t)^3]^2[(4r2t)3]2?

1 Answer
Feb 8, 2017

See the entire simplification process below:

Explanation:

First, simplify the outer brackets using this rule for exponents:

(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))(xa)b=xa×b

[(4r^2t)^color(red)(3)]^color(blue)(2) = (4r^2t)^(color(red)(3) xx color(blue)(2)) = (4r^2t)^6[(4r2t)3]2=(4r2t)3×2=(4r2t)6

Now we can use the above rule and this rule to complete the simplification:

a = a^color(red)(1)a=a1

(4r^2t)^6 = (4^color(red)(1)r^2t^color(red)(1))^6 = 4^(color(red)(1) xx color(blue)(6))r^(color(red)(2) xx color(blue)(6))t^(color(red)(1) xx color(blue)(6)) = 4^6r^12t^6 =(4r2t)6=(41r2t1)6=41×6r2×6t1×6=46r12t6=

4096r^12t^64096r12t6