SOLUTION: ∛2x× ∛(4x^2 y^2 )×∛(2y^(4 ) ) how to simplify?

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Question 487007: ∛2x× ∛(4x^2 y^2 )×∛(2y^(4 ) )
how to simplify?

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
root%283%2C2x%29%2Aroot%283%2C4x%5E2y%5E2%29%2Aroot%283%2C2y%5E4%29

Write all as one cube root:

root%283%2C%282x%29%284x%5E2y%5E2%29%282y%5E4%29%29

Break everything into prime factors:

root%283%2C%282x%29%2A%282%2A2xxyy%29%282yyyy%29%29

Remove the parentheses:

root%283%2C2x2%2A2xxyy2yyyy%29%29

Rearrange, putting like factors together:

root%283%2C2%2A2%2A2%2A2xxxyyyyyy%29

Since the index of a cube root is 3, group
like factors by 3's:

root%283%2C%282%2A2%2A2%29%2A2%28xxx%29%28yyy%29%28yyy%29%29

Write each group of 3 as a cube:

root%283%2C%282%5E3%29%2A2%28x%5E3%29%28y%5E3%29%28y%5E3%29%29

Write as a product of cube roots:



To take the cube root of a cube, eliminate the radical and the exponent:

2%2A%28root%283%2C2%29%29%2Axyy

2xy%5E2%2Aroot%283%2C2%29

Edwin