Question

How do you simplify `(x^3)^4`?

Answer 1

You have to follow exponent laws in order to find the answer.

Explanation:

`(x^3)^4`
Becomes:

`x^(3*4)`

`= x^12`

Answer 2

The answer is `x^12`.

Explanation:

Write out the whole power of `4`, then add up the exponents using the exponent addition rule. I color-coded some of the problem so that it is easier to see:

`color(white)=(x^3)^4`

`=(x^color(red)3)(x^color(yellow)3)(x^color(green)3)(x^color(blue)3)`

`=x^color(red)3*x^color(yellow)3*x^color(green)3*x^color(blue)3`

`=x^(color(red)3+color(yellow)3)*x^color(green)3*x^color(blue)3`

`=x^color(orange)6*x^color(green)3*x^color(blue)3`

`=x^(color(orange)6+color(green)3)*x^color(blue)3`

`=x^color(brown)9*x^color(blue)3`

`=x^(color(brown)9+color(blue)3)`

`=x^12`