How do you simplify #root4(x^16)#?

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Answer 1 · 2018-07-04T20:11:07

Simplifying this root gives us #x^4#

So you can think of this as how many group of 4 can make 16.

So what gives us #x^16#? The answer is 4 because 4 x 4 = 16.

Answer 2 · 2018-07-04T20:19:25

#x^4#

We can rewrite the monomial under the radical

#(x^4)^4#, which allows us to rewrite the entire expression as

#rootcolor(blue)(4)((x^4)^color(blue)(4))#

The fourth root cancels with the fourth power, and we're left with

#x^4#

Hope this helps!