SOLUTION: Rationalize the denominator: 2y/cube root of 16x^5 y^2 Thank you

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Question 1037521: Rationalize the denominator:
2y/cube root of 16x^5 y^2
Thank you
Found 2 solutions by ankor@dixie-net.com, Alan3354:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalize the denominator:
%282y%29%2F%283sqrt%2816x%5E5%2Ay%5E2%29%29=%282y%29%2F%283sqrt%288%2A2%2Ax%5E3%2Ax%5E2%2Ay%5E2%29%29
extract the cube root of 8 and cube root of x^3 cancel the 2
%282y%29%2F%282x%2A3sqrt%282x%5E2%2Ay%5E2%29%29 = y%2F%28x%2A3sqrt%282x%5E2%2Ay%5E2%29%29
multiply by the denominator over itself
y%2F%28x%2A3sqrt%282x%5E2%2Ay%5E2%29%29 * %28x%2A3sqrt%282x%5E2y%5E2%29%29%2F%28x%2A3sqrt%282x%5E2y%5E2%29%29
%28xy%2A3sqrt%282x%5E2y%5E2%29%29%2F%28x%5E2%282x%5E2y%5E2%29%29 = %28xy%2A3sqrt%282x%5E2y%5E2%29%29%2F%282x%5E4y%5E2%29%29
cancel xy
%283sqrt%282x%5E2y%5E2%29%29%2F%282x%5E3y%29%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalize the denominator:
2y/cube root of 16x^5 y^2
------
2y%2Froot%283%2C16x%5E5y%5E2%29
Factor out the 8
= 2y%2F2root%283%2C2x%5E5y%5E2%29
= y%2Froot%283%2C2x%5E5y%5E2%29
----
= y%2Aroot%283%2C4xy%29%2Froot%283%2C2x%5E5y%5E2%2A4xy%29
= y%2Aroot%283%2C4xy%29%2Froot%283%2C8x%5E6y%5E3%29
= y%2Aroot%283%2C4xy%29%2F%282x%5E2y%29
= root%283%2C4xy%29%2F2x%5E2