Originally Posted by

**harish21** Course: Advanced Calculus aka Real Analysis

Prove that, for a positive number$\displaystyle x$ and integers $\displaystyle m $and $\displaystyle n$,

$\displaystyle (x^{\frac{1}{n}})^m = (x^m)^{\frac{1}{n}}$

How is this proof done?

I tried this:

$\displaystyle (x^{\frac{1}{n}})^m = (x^{\frac{1}{kn}})^{km}$

for $\displaystyle u > 0$

$\displaystyle u^k = [(u^{\frac{1}{n}})^n]^k = (u^{\frac{1}{n}})^{nk}$

then i tried to set $\displaystyle u = x^m$ and got completely lost.

Can anyone tell if I was doing it correctly or show some steps on how to do this ?