Question: Simplification of (ln(x)^n)^(1/n)

I use  Maple 2015 and I try to understand how the simplification rules apply in the case of the expression 

f := n -> (ln(x)^n)^(1/n)

Here n is assumed to be a strictly positive and I consider only the cases "n is an integer" or "1/n is an integer".

All the questions are orange written in the attached file and resumed below:

1. Why simplify(f(2)) simplifies f(2) whereas simplify(f(n)) doesn't simplifies f(n) for any integer n > 2?
    
2. Why simplify(f(1/n)) simplifies f(1/n)?
    
3. Why simplify(f(3)) with adhoc assumptions returns a simplified expression of some form whereas, for any integer n > 3,  simplify(f(n)) with (the same corresponding) adhoc assumptions returns a simplified expression of a complete different form than with n=3?

Can you please have a look to it and give me some clarifications?
Simplification_rules.mw

Thanks in advance