Conjecture: $2^{\frac{1}{\log_2(x)}}$ is algebraic iff $x=2^n$ or $1/2^n$ for some $n\in \Bbb Q^+.$

How can I prove my conjecture?

It might be very easy to prove but I am stuck at the moment.

If for example $x=6$ then I think the expression fails to be algebraic due to the fact that $6$ cannot be expressed the above forms.