Problem Statement

This task will demonstrate the order of exponentiation   (xy)   when there are multiple exponents. (Many programming languages,   especially those with extended─precision integer arithmetic,   usually support one of **, ^, ↑ or some such for exponentiation.)

Show the result of a language's evaluation of multiple exponentiation (either as an integer or floating point). If your language's exponentiation operator is not one of the usual ones, please comment on how to recognize it.

Using whatever operator or syntax your language supports (if any), show the results in three lines (with identification):

If there are other methods (or formats) of multiple exponentiations, show them as well.

Let's start with the solution:

#lang racket
;; 5**3**2 depends on associativity of ** : Racket's (scheme's) prefix function
;; calling syntax only allows for pairs of arguments for expt.

;; So no can do for 5**3**2
;; (5**3)**2
(displayln "prefix")
(expt (expt 5 3) 2)
;; (5**3)**2
(expt 5 (expt 3 2))

;; There is also a less-used infix operation (for all functions, not just expt)... which I suppose
;; might do with an airing. But fundamentally nothing changes.
(displayln "\"in\"fix")
((5 . expt . 3) . expt .  2)
(5  . expt . (3 . expt . 2))

;; everyone's doing a reduction, it seems
(displayln "reduction")
(require (only-in srfi/1 reduce reduce-right))
(reduce expt 1 '(5 3 2))
(reduce-right expt 1 '(5 3 2))