Nice catch! Just to be clear, it was that we were incrementing our exponent but not our counter, is that right? I pushed up a fix, but let me know if there were other issues.

It's a bit more involved than that.

  mul rcx, rax       ; multiply our result by our base, save into rcx

This should probably be using rbx, since that's the designated base, not rax, which is the exponent.

In the explanation just above, there's a 2*8 step missing, while this one is incorrect:

  4. result = 16 * 2, result is now 16

Since 2*16 is not 16.

Ahhhhh thank you! Do you mind opening a PR or issue so I can get to that? Thank you for noticing!!