SOLUTION: divide, and if possible, simplify. {{{root(3,250(x^5)(y^3))/root(3,2x^3)}}} please help!

Algebra ->  Rational-functions -> SOLUTION: divide, and if possible, simplify. {{{root(3,250(x^5)(y^3))/root(3,2x^3)}}} please help!      Log On


   

Question 34332: divide, and if possible, simplify.
root%283%2C250%28x%5E5%29%28y%5E3%29%29%2Froot%283%2C2x%5E3%29
please help!
Answer by mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
Hello!
Since both the numerator and the denominator have been applied the same radical (cubic root), you can join them in the following way:

Now simplifying the 250 and the 2 leaves 125 in the numerator:
root%283%2C%28125%28x%5E5%29%28y%5E3%29%29%2F%28x%5E3%29%29
Also, x%5E5%2Fx%5E3+=+x%5E%285-3%29+=+x%5E2, so we get:
root%283%2C%28125%28x%5E2%29%28y%5E3%29%29%29
Finally, since we have a multiplication of terms, we can apply the cubic root to each of them:

Since the cubic root of 125 is 5, and the cubic root of y^3 is y, we get:
5%2Aroot%283%2Cx%5E2%29%2Ay
Finally, root%283%2Cx%5E2%29+=+x%5E%282%2F3%29, so the final expression is:
5%2Ax%5E%282%2F3%29%2Ay

I hope this helps!
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