I am trying to solve this limit:
$$\lim\_{x\to\infty} \frac{2^x}{x^{200}}$$

The first result is an indetermination of the kind $\frac{\infty}{\infty}$ but here applying L'Hopital would be too long, I do not see any substitution by means of equivalent infinitesimals possible and simplifying the limit neither.

How can I solve it? The solution must be $\infty$. Thank you!