Compare the growth of $2^{n}$ to $n^{a}$ for all $a \in \mathbb{N}$? How to find which of $2^{n}$ to $n^{a}$ is an (upper bound, tight bound asymptotically larger, etc..)? I tried to use the formula:

$$ \lim_{n\to\infty} \frac{f(n)}{g(n)} $$

where $f(n) = n^{a}$ and $f(n) = 2^{n}$

But I cannot figure out how to use L'Hospital's rule to solve it.  We are guaranteed that $a \in \mathbb{N}$.
As a hint, $n^\alpha = 2^{\alpha \log_2 n}$. Now, you can compute the ratio between these functions by subtracting the exponents. There's no need to use l'Hôpital's rule.