Why do this problem?
It gives practice in working with inequalities. As we know

n

is a positive integer learners can investigate

n^{\frac{1}{n}}

for for different values of

n

and make conjectures about where the maximum value occurs.

Possible approach
You need to find a local maximum for a small value of $n$ and then prove that this is the only maximum value. Clearly it is impossible to check all values of $n$ . One method of proving the result uses the Binomial theorem.

Key questions