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

1 Answer
smendyka
Feb 4, 2017

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)#

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