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

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Answer 1 · 2017-02-04T04:50:39

See the entire simplification process below:

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: $(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))$

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

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