Define the exponentiation operator on naturals recursively so that x0 = 1 and xS(y) = xy · x. Prove by induction, using this definition, that for any naturals x, y, and z, xy+z = xy · xz and xy·z = (xy)z.

Jack is considering a list of features and fees for current bank: jack plans on using network atms about 4 times per month. what would be jack’s total estimated annual fees for a checking account with direct paycheck deposit, one overdraft per year, and no 2nd copies of statements? a. $44 b. $104 c. $144 d. $176