SOLUTION: I need help on figuring out how to remove the radical from the denominator. The problem I have is: The 5th root of s to the power of 10 over the 5th root of t to the power of 2

Algebra ->  Square-cubic-other-roots -> SOLUTION: I need help on figuring out how to remove the radical from the denominator. The problem I have is: The 5th root of s to the power of 10 over the 5th root of t to the power of 2      Log On


   

Question 724418: I need help on figuring out how to remove the radical from the denominator.
The problem I have is:
The 5th root of s to the power of 10 over the 5th root of t to the power of 20.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
root%285%2Cs%5E10%29=root%285%2Cs%5E%282%2A5%29%29=root%285%2C%28s%5E2%29%5E5%29=s%5E2 and root%285%2Cs%5E20%29=root%285%2Cs%5E%284%2A5%29%29=root%285%2C%28s%5E4%29%5E5%29=s%5E4
So root%285%2Cs%5E10%29%2Froot%285%2Cs%5E20%29=s%5E2%2Fs%5E4=1%2Fs%5E2
You did not need to do anything eliminate to remove the radical from the denominator in this case.
Also quotients of roots of the same index equal the root of the quotient, as in
,
which would not help that much in this case, but could help in other cases.

If you really have to get rid of a single radical in the denominator, multiply numerator and denominator times another radical, such that the product will simplify, as in
or