[1] This is a conceptual description of what power's return value is; it is not how power is actually implemented. If power were implemented that way then it would require n-1 multiplications, which would be grossly inefficient. Power is implemented using the "Russian peasant algorithm", which requires only O(log n) multiplications. See section 4.6.3 of Knuth (D. E. Knuth, The Art of Computer Programming. Volume 2: Seminumerical Algorithms, Addison-Wesley, 1981) for a discussion.

[2] See the Monoid Operation requirements for a discussion of associativity.

[3] This is in fact not the minimum possible number of multiplications: it is possible to compute the fifteenth power of x using only five multiplications, but power(x, 15) uses six.