continuity - Find all multiplicative continuous functions on $(0,infty)$

If $x>0,y>0$ and if $f(xy)=f(x)f(y)$, then $f=\, ?$

I tried the problem. And got it as $f(x)^n=f(x^n)$.
But answer is $f(x)=x^n$. How?
$f$ is a continuous function.