Question

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

Answer 1

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))`

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

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

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

`(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 =`

`4096r^12t^6`