How do you simplify #root4((3x^2)^4)#?

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Answer 1 · 2016-05-25T13:49:43

Rewrite to get rid of the root sign to make it easier to work with and get to #3x^2#

Let's first start with the original:

#root(4)((3x^2)^4)#

Now let's rewrite this to get rid of the root sign (I find working with fractional exponents to be easier):

#((3x^2)^4)^(1/4)#

When we take things that have an exponent and take them to a power, the 2 exponents multiply together, like this:

#(3x^2)^(4*(1/4))#

#(3x^2)^1#

#3x^2#