SOLUTION: (5th root of 2x^2y)^3

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Question 427266: (5th root of 2x^2y)^3
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i'm assuming you want to simplify this as much as possible.

you are starting off with %28root%285%2C2x%5E2y%29%29%5E3

root%285%2C2x%5E2y%29 is the same as %282x%5E2y%29%5E%281%2F5%29

your expression becomes:

%28%282x%5E2y%29%5E%281%2F5%29%29%5E3

since, in general, %28a%5Eb%29%5Ec+=+a%5E%28b%2Ac%29, then your expression becomes:

%282x%5E2y%29%5E%283%2F5%29

singe, in general,

%28a%5Eb%2Ac%5Ed%2Ae%5Ef%29%5Eg+=+a%5E%28b%2Ag%29%2Ac%5E%28d%2Ag%29%2Ae%5E%28f%2Ag%29, then your expression becomes:

2%5E%283%2F5%29%2A%28x%5E2%29%5E%283%2F5%29%2Ay%5E%283%2F5%29

this simplifies to:

2%5E%283%2F5%29%2Ax%5E%286%2F5%29%2Ay%5E%283%2F5%29

if you can't see it because it is cut off, the exponent over the 2 is 3/5, and the exponent over the x is 6/5 and the exponent over the y is 3/5.

i have confirmed that the original expression and the final expression are equivalent.

if that's what you were asking about, then this should be your answer.