You are even closer now!

What the type checker is trying to tell you is that it doesn't know how to raise Maybe Integer to some power.

You apply the ^ operator to two values, f2Maybe (n `div` 2) and 2. Let us give them names:

let a = f2Maybe (n `div` 2) :: Maybe Integer

    b = 2 :: Int

in a ^ b

You see that the type of a is Maybe Integer. What does this mean? There are only 2 cases to consider. You have Just an integer or you have Nothing.

You can use the case construct to write the code for both cases.

f2Maybe :: Integer -> Maybe Integer
f2Maybe n
   | n > 0  = Nothing
   | n == 0  = Just 1
   | even n = case f2Maybe (n `div` 2) of

                Just x -> <fill in>

                Nothing -> <fill in>
   | odd n  = case f2Maybe (n `div` 2) of

                Just x -> <fill in>

                Nothing -> <fill in>