Project 1 - difference between Exercise 8 and gcd function/algorithm

After Claim 2 is written that the output of the GCD algorithm is given in the form base2^pow, and the code seems to give the same thing. However, exercise 8 asks the output to be given in a base^e form, and the implementation of debug seems to give baseexponent. Are we supposed to convert between two types, or is there a mistake?

example of an input-output sets.
Screenshot from 2023-04-28 16-03-51

another input-output set since the site limits me to one media file per post
Screenshot from 2023-04-28 16-10-23

You are absolutely correct. There was a typo in Preliminary Exercise 8, thanks for pointing it out.
The left hand side of the equation in the functionality there is supposed to be \langle \mathit{base} \rangle \cdot 2^e, not \langle \mathit{base} \rangle^e. The project PDF is fixed now.