Irrational function

Question

$(1)$If $f(x)=x^n$ and $g(x)=x^\frac{1}{n} $,then $f(x)$ and $g(x)$ are the inverse of each other.

$(2)$ therefore $f(x) = x^n$ and $g(x) = x^\frac{1}{n}$ is the mirror image about $y=x$ Now how $(2)$ follows from $(1)$

How to prove it?