SOLUTION: 4th root of x^3 Y^5 z^8

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Question 594103: 4th root of x^3 Y^5 z^8
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
root%284%2C+x%5E3y%5E5z%5E8%29

Rules for root%28N%2CB%5EM%2A%22%28OTHER_FACTORS_IF_ANY%29%22%29

1. If M is less than N, then leave it as it is.

2. If M can be divided evenly by N, then it equals 
matrix%282%2C1%2C%22%22%2CB%5E%28M%2FN%29%29%2A%22%22root%28N%2C%22%28OTHER_FACTORS_IF_ANY%29%22%29

3. If M is greater than N, then do this division
where Q is the quotient and R is the remainder 

       Q
     N)M
       ...
        R  

Then it equals:

B%5EQ%2A%22%22root%28N%2CB%5ER%2A%22%28OTHER_FACTORS_IF_ANY%29%22%29

root%284%2C+x%5E3y%5E5z%5E8%29

For the x³, since 3 is less than 4, we use rule 1 and do nothing 

For they y5, since 5 is greater than 4, we use rule 3
and do this division:
        
       1 
     4)5
       4
       1

and write:

y%5E1%2Aroot%284%2C+x%5E3y%5E1z%5E8%29 and dispose of the 1 exponents:

y%2Aroot%284%2C+x%5E3yz%5E8%29
     
For the z8, since 8 can be divided evenly by 4, we
use rule 2 and we end up with

yz%5E2%2Aroot%284%2C+x%5E3y%29

Edwin