SOLUTION: Z^m/n = z^m*1/n = (z^1/n)^m = (n/square root of z)^m. What is the reasoning behind each step? I'm really not understanding how they get from one step to the next.

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Z^m/n = z^m*1/n = (z^1/n)^m = (n/square root of z)^m. What is the reasoning behind each step? I'm really not understanding how they get from one step to the next.      Log On


   

Question 263082: Z^m/n = z^m*1/n = (z^1/n)^m = (n/square root of z)^m.
What is the reasoning behind each step? I'm really not understanding how they get from one step to the next.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
z%5E%28m%2Fn%29=z%5E%28m%2A%281%2Fn%29%29%5E%22%22 Use the property that a%2Fb=a%281%2Fb%29


z%5E%28m%2Fn%29=z%5E%28%281%2Fn%29m%29%5E%22%22 Commute (ie swap) the terms.


z%5E%28m%2Fn%29=%28z%5E%281%2Fn%29%29%5Em%5E%22%22 Use the identity x%5E%28y%2Az%29=%28x%5E%28y%29%29%5Ez.


z%5E%28m%2Fn%29=%28root%28n%2Cz%29%29%5Em%5E%22%22 Convert to radical notation. Remember that x%5E%28m%2Fn%29%5E%22%22=root%28n%2Cx%5Em%29