;;;  N-to-the-K
;;; ----------------------------------------
;;;  INPUTS:  N, K, non-negative integers (not both 0)
;;;  OUTPUT:  the value of N to the Kth power

(define n-to-the-k
  (lambda (n k)
    ;; Call the accumulator-based tail-recursive helper function
    ;; with an appropriately initialized accumulator
    (n-to-the-k-acc n k 1)))

;;;  N-to-the-K-acc
;;; ----------------------------------------
;;;  INPUTS:  N, K, as above
;;;           ACC, a multiplicative accumulator
;;; ----------------------------------------
;;;  Can use K as a counter (the number of times N is multiplied)

(define n-to-the-k-acc
  (lambda (n k acc)
    (cond
      ;; Base Case:  K = 0
      ((<= k 0)
       ;; return the accumulator
       acc)
      ;; TAIL-Recursive Case:  K > 0
      (#t
       ;; tail-recursive function call with updated inputs
       (n-to-the-k-acc n
                       (- k 1)
                       (* acc n))))))


;;;  N-To-the_k
;;; ----------------------------


(define n-to-the-k-alt
  (lambda (n k)
    (local [(define acc 1)]
      (dotimes (i k)
               (set! acc (* acc n)))
      ;; return the value of the accumulator
      acc)))