How to show that $G=\mathrm{Gal}[\Bbb Q(\xi_{2^n})/\Bbb Q(\xi_{2^m})]$ cyclic?

Question

How to show that $G=\mathrm{Gal}[\Bbb Q(\xi_{2^n})/\Bbb Q(\xi_{2^m})]$ cyclic? $n>m>1$ are natural numbers. $\xi_{2^n}$ and $\xi_{2^m}$ are cyclotomic roots.

I know that the order of $ G $ is $|G|=2^{n-m}$