20 points

Find the exact number of bit multiplications required to find the nth power of a b-bit integer directly from the recursive definition of exponentiation, assuming that the kth power of a b-bit number has bk bits, and that multiplication of a b-bit number by a c-bit number has cost exactly bc.
Redo the problem above, assuming that the divide-and-conquer algorithm is used for exponentiation, and that n is a power of 2.
Redo the problem above, assuming that n is one less than a power of 2.