Course: Advanced Calculus aka Real Analysis
Prove that, for a positive number and integers and ,
How is this proof done?
I tried this:
for
then i tried to set and got completely lost.
Can anyone tell if I was doing it correctly or show some steps on how to do this ?
This is what the book has stated:
Definition: For and rational number , where m and n are integers, with n positive, we define
since rational numbers can be expressed in different ways as quotients of integers, we need to establish that if m is an integer and n and k are natural numbers then,
.......(1)
Since, for u>0,
,
setting , we have
, from which (1) follows and so rational powers are properly defined.
Thats all the book has given about rational power and asked us to verfify the question I posted.