SOLUTION: Simplify by taking roots of the numerator and the demoninator. Assume that all expressions under radicals represent positive numbers. The square root of 243x^6/y^20 to the fifth

Algebra ->  Square-cubic-other-roots -> SOLUTION: Simplify by taking roots of the numerator and the demoninator. Assume that all expressions under radicals represent positive numbers. The square root of 243x^6/y^20 to the fifth       Log On


   

Question 307105: Simplify by taking roots of the numerator and the demoninator. Assume that all expressions under radicals represent positive numbers.
The square root of 243x^6/y^20 to the fifth root.
Here is what I have so far: the square root of 243x^6 to the fifth root divided by the square root of 4^20 to the fifth root.
This is the answer that I got but I'm sure it is wrong.
3x^4 x^2 to the fifth root divided by y^4.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not exactly sure what your problem is. Do you mean the FIFTH root of the given fraction?

That is, root%285%2C+%28243x%5E6%29%2F%28y%5E20%29%29?

If so, then you are almost correct. Notice that 243 is actually 3^5, and also notice that to be a perfect 5th power, a power must be divisible by 5. I would start by making TWO 5th roots. Place the perfect 5th powers in one 5th root, and leftover factors in the second 5th root.

root%285%2C+_____%29%2Aroot%285%2C_____%29

Sorting it out looks like this:
+root%285%2C+%28243x%5E5%29%2F%28y%5E20%29%29%2Aroot%285%2Cx%29+
%28%283x%29%2F%28y%5E4%29%29%2Aroot%285%2Cx%29+

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus