Question

How do you simplify `\root [ 3] { 2x ^ { 6} }`?

Answer 1

See the entire simplification process below:

Explanation:

First, use this rule for radicals and exponents to rewrite this expression: `root(color(red)(n))(x) = x^(1/color(red)(n))`

`root(color(red)(3))(2x^6) = (2x^6)^(1/color(red)(3))`

Now use these rules for exponents to further simplify:

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

`(2x^color(red)(6))^(1/color(blue)(3)) = (2^color(red)(1)x^color(red)(6))^(1/color(blue)(3)) =2^(color(red)(1) xx color(blue)(1/3))x^(color(red)(6) xx color(blue)(1/3)) = 2^(1/3)x^(6/3) =`

`2^(1/3)x^2` or `root(3)(2)x^2` or `1.2599x^2` rounded to the nearest ten thousandth.