Question

How do you simplify `root3(x^4)`?

Answer 1

See the entire simplification process below:

Explanation:

The first simplification step will use this rule for exponents in radical form: `root(color(red)(n))(x) = x^(1/color(red)(n))`

So we can rewrite this expression as:

`root(color(red)(3))(x^4) = (x^4)^(1/color(red)(3))`

We can now use this rule for exponents to complete the simplification: `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`(x^color(red)(4))^color(blue)(1/3) = x^(color(red)(4) xx color(blue)(1/3)) = x^(4/3)`