Question

How do you simplify `(4a^3)^2` and write it using only positive exponents?

Answer 1

See the entire simplification process below:

Explanation:

Use these two rules of exponents to simplify this expression:

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

`(4a^3)^2 = (4^color(red)(1)a^color(red)(3))^color(blue)(2) = 4^(color(red)(1) xx color(blue)(2))a^(color(red)(3) xx color(blue)(2)) = 4^2a^6 = 16a^6`

Answer 2

`color(blue)(16a^6`

Explanation:

`(4a^3)^2`

`:.(m^m)^n=m^(m xx n)`

`:.4^2a^6`

`:.color(blue)(16a^6`