SOLUTION: cube root of 125^8/cube root of y^3

Algebra ->  Square-cubic-other-roots -> SOLUTION: cube root of 125^8/cube root of y^3      Log On


   

Question 421411: cube root of 125^8/cube root of y^3
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
root%283%2C+125%5E8%29%2Froot%283%2C+y%5E3%29
A fact about radicals that will help us with this problem is
root%28p%2C+a%5Eq%29+=+%28root%28p%2C+a%29%29%5Eq
This helps us because 5%5E3+=+125 so root%283%2C+125%29+=+5. So if we can find the cube root before we raise to the 8th power, it will be easier:
%28root%283%2C+125%29%29%5E8%2Froot%283%2C+y%5E3%29
The two cube roots simplify giving us:
5%5E8%2Fy
This may be an acceptable form for the answer. If not, then get out your calculator and figure out 5%5E8.