SOLUTION: Please walk me through each step: Rationalize the denominator: 3x divided by index 5 root of 2x^2y^3. They say answer is 3 times index 5 root of 16x^3y^2 divided by 2y

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Question 200941: Please walk me through each step: Rationalize the denominator:
3x divided by index 5 root of 2x^2y^3. They say answer is 3 times index 5 root of 16x^3y^2 divided by 2y
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalize the denominator:
3x divided by index 5 root of 2x^2y^3. They say answer is 3 times index 5 root of 16x^3y^2 divided by 2y
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Rewrite the problem as:
(3x)/(2x^2y^3)^(1/5)
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Multiply numerator and denominator by 2^(4)*x^(3)*y^(2) to get:
{(3x)[2^(4)*x^(3)*y^(2)]^(1/5)/[2^5*x^5*y^5]^(1/5)
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Simplify:
{(3x)[(2^(4)*x^(3)*y^(2)]^(1/5)/[2xy]
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Cancel the "x" factor to get:
= [3[(2^(4)*x^(3)*y^(2)]^(1/5)/[2y]
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Cheers,
Stan H.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3x divided by index 5 root of 2x^2y^3
=3x%2F%282x%5E2y%5E3%29%5E%281%2F5%29
Multiply NUM and DEN by %282x%5E2y%5E3%29%5E%284%2F5%29
= 3x%2A%282x%5E2y%5E3%29%5E%284%2F5%29%2F2x%5E2y%5E3
Cancel the x's and expand the 4th power.
= 3%2A%2816x%5E8y%5E12%29%5E%281%2F5%29%2F2xy%5E3
Take the x^5y^10 out of the 1/5 power
= 3xy%5E2%2A%2816x%5E3y%5E2%29%5E%281%2F5%29%2F2xy%5E3
Cancel the xy^2
= 3%2A%2816x%5E3y%5E2%29%5E%281%2F5%29%2F2y