Zero to the zero power: Difference between revisions

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Some computer programming languages are not exactly consistent (with other computer programming languages)
when raising zero to the zeroth power: 0⁰

Task

Show the results of raising zero to the zeroth power.

If your computer language objects to 0**0 or 0^0 at compile time, you may also try something like:

           x = 0
           y = 0
           z = x**y
           say  'z='  z

Show the result here.
And of course use any symbols or notation that is supported in your computer programming language for exponentiation.

See also

The Wiki entry: Zero to the power of zero.
The Wiki entry: Zero to the power of zero: History.
The MathWorld™ entry: exponent laws.
- Also, in the above MathWorld™ entry, see formula (9): $x^{0}=1$ .
The OEIS entry: The special case of zero to the zeroth power

Action!

Library: Action! Tool Kit

INCLUDE "D2:REAL.ACT" ;from the Action! Tool Kit

PROC Main()
  REAL z,res

  Put(125) PutE() ;clear the screen

  IntToReal(0,z)
  Power(z,z,res)

  PrintR(z) Print("^")
  PrintR(z) Print("=")
  PrintRE(res)
RETURN

Output:

Screenshot from Atari 8-bit computer

0^0=.9999999998

Ada

with Ada.Text_IO, Ada.Integer_Text_IO, Ada.Long_Integer_Text_IO,
  Ada.Long_Long_Integer_Text_IO, Ada.Float_Text_IO, Ada.Long_Float_Text_IO,
  Ada.Long_Long_Float_Text_IO;
use  Ada.Text_IO, Ada.Integer_Text_IO, Ada.Long_Integer_Text_IO,
  Ada.Long_Long_Integer_Text_IO, Ada.Float_Text_IO, Ada.Long_Float_Text_IO,
  Ada.Long_Long_Float_Text_IO;

procedure Test5 is

   I    : Integer           := 0;
   LI   : Long_Integer      := 0;
   LLI  : Long_Long_Integer := 0;
   F    : Float             := 0.0;
   LF   : Long_Float        := 0.0;
   LLF  : Long_Long_Float   := 0.0;
   Zero : Natural           := 0;

begin
   Put ("Integer           0^0 = "); 
   Put (I ** Zero, 2);   New_Line;
   Put ("Long Integer      0^0 = ");
   Put (LI ** Zero, 2);  New_Line;
   Put ("Long Long Integer 0^0 = ");
   Put (LLI ** Zero, 2); New_Line;
   Put ("Float           0.0^0 = ");           
   Put (F ** Zero);   New_Line;
   Put ("Long Float      0.0^0 = ");      
   Put (LF ** Zero);  New_Line;
   Put ("Long Long Float 0.0^0 = "); 
   Put (LLF ** Zero); New_Line;
end Test5;

Output:

Integer           0^0 =  1
Long Integer      0^0 =  1
Long Long Integer 0^0 =  1
Float           0.0^0 =  1.00000E+00
Long Float      0.0^0 =  1.00000000000000E+00
Long Long Float 0.0^0 =  1.00000000000000000E+00

ALGOL 68

Works with: ALGOL 68G version Any - tested with release 2.6.win32

print( ( 0 ^ 0, newline ) )

Output:

+1

APL

      0*0
1

AppleScript

 return 0 ^ 0

Output:

1.0

Applesoft BASIC

]? 0^0
1

Arturo

print 0 ^ 0
print 0.0 ^ 0

Output:

1
1.0

Asymptote

write("0 ^ 0 = ", 0 ** 0);

BaCon

PRINT POW(0, 0)

Output:

prompt$ ./zerotothezero
1

BASIC

BASIC256

print "0 ^ 0 = "; 0 ^ 0

Chipmunk Basic

10 print "0 ^ 0 = ";0^0

MSX Basic

10 PRINT "0 ^ 0 = "; 0 ^ 0

QBasic

Works with: QBasic version 1.1

Works with: QuickBasic version 4.5

PRINT "0 ^ 0 ="; 0 ^ 0

Run BASIC

Works with: Just BASIC

Works with: Liberty BASIC

print "0 ^ 0 = "; 0 ^ 0

True BASIC

Works with: QBasic

PRINT "0 ^ 0 ="; 0 ^ 0
END

XBasic

Works with: Windows XBasic

PROGRAM	"progname"
VERSION	"0.0000"

IMPORT	"xma"   'required for POWER

DECLARE FUNCTION  Entry ()

FUNCTION  Entry ()
    PRINT "0 ^ 0 = "; 0 ** 0
    PRINT "0 ^ 0 = "; POWER(0, 0)
END FUNCTION
END PROGRAM

ZX Spectrum Basic

PRINT 0↑0

Output:

1

0 OK, 0:1

Befunge-93 doesn't have explicit support for exponentiation, but there are a couple of fingerprint extensions for Befunge-98 which add that functionality. The example below makes use of the FPDP fingerprint (double precision floating point).

Note that the result is potentially dependent on the underlying language of the interpreter, but all those tested so far have returned 1. Interpreters that don't support Befunge-98, or don't support this fingerprint, should just terminate (possibly with a warning).

"PDPF"4#@(0F0FYP)@

Output:

1.000000

Binary Lambda Calculus

In lambda calculus, \n. n n is a function mapping a Church numeral n to the Church numeral n^n. The following BLC program computes this for n=0 by using its empty input as a Church numeral (since nil coincides with Church numeral 0), and outputting in unary (i.e as a string of 0^0 1s), as generated from https://github.com/tromp/AIT/blob/master/rosetta/exp00.lam :

0001010110100000010110111011010

Output:

BQN

BQN doesn't specify the details of arithmetic functions; existing implementations use IEEE doubles and the pow function, giving a result of 1.

0⋆0

Output:

Bracmat

0^0

Output:

Burlesque

blsq ) 0.0 0.0?^
1.0
blsq ) 0 0?^
1

C

Works with: C99

This example uses the standard pow function in the math library. 0^0 is given as 1.

#include <stdio.h>
#include <math.h>
#include <complex.h>

int main()
{
	printf("0 ^ 0 = %f\n", pow(0,0));
        double complex c = cpow(0,0);
	printf("0+0i ^ 0+0i = %f+%fi\n", creal(c), cimag(c));
	return 0;
}

Output:

0 ^ 0 = 1.000000
0+0i ^ 0+0i = nan+nani

C#

using System;

namespace ZeroToTheZeroeth
{
    class Program
    {
        static void Main(string[] args)
        {
            double k = Math.Pow(0, 0);
            Console.Write("0^0 is {0}", k);           
        }
    }
}

Output:

0^0 is 1

C++

#include <iostream>
#include <cmath>
#include <complex>

int main()
{
  std::cout << "0 ^ 0 = " << std::pow(0,0) << std::endl;
  std::cout << "0+0i ^ 0+0i = " <<
    std::pow(std::complex<double>(0),std::complex<double>(0)) << std::endl;
  return 0;
}

Output:

0 ^ 0 = 1
0+0i ^ 0+0i = (nan,nan)

Caché ObjectScript

ZEROPOW
  // default behavior is incorrect:
  set (x,y) = 0
  w !,"0 to the 0th power (wrong): "_(x**y)  ; will output 0
  
  // if one or both of the values is a double, this works
  set (x,y) = $DOUBLE(0)
  w !,"0 to the 0th power (right): "_(x**y)
  
  quit

Output:

SAMPLES>do ^ZEROPOW
0 to the 0th power (wrong): 0

0 to the 0th power (right): 1

Clojure

user=> (use 'clojure.math.numeric-tower)
user=> (expt 0 0)
1

; alternative java-interop route:
user=> (Math/pow 0 0)
1.0

CLU

The CLU reference manual doesn't mention the issue, so the fact that it returns 1 in my case could just be an implementation detail.

start_up = proc ()
    zz_int: int := 0 ** 0
    zz_real: real := 0.0 ** 0.0
    
    po: stream := stream$primary_output()
    stream$putl(po, "integer 0**0: " || int$unparse(zz_int))
    stream$putl(po, "real 0**0: " || f_form(zz_real, 1, 1))
end start_up

Output:

integer 0**0: 1
real 0**0: 1.0

COBOL

identification division.
program-id. zero-power-zero-program.
data division.
working-storage section.
77  n                         pic 9.
procedure division.
    compute n = 0**0.
    display n upon console.
    stop run.

Output:

ColdFusion

Classic tag based CFML

<cfset zeroPowerTag = 0^0>
<cfoutput>"#zeroPowerTag#"</cfoutput>

Output:

"1"

Script Based CFML

<cfscript>
  zeroPower = 0^0;
  writeOutput( zeroPower );
</cfscript>

Output:

Commodore BASIC

Commodore computers use the up arrow key ↑ as the exponent operator.

Output:

ready.
print 0↑0
1

ready.
█

Common Lisp

> (expt 0 0)
1

Crystal

puts "Int32:            #{0_i32**0_i32}"
puts "Negative Int32:   #{-0_i32**-0_i32}"
puts "Float32:          #{0_f32**0_f32}"
puts "Negative Float32: #{-0_f32**-0_f32}"

Output:

Int32:            1
Negative Int32:   1
Float32:          1.0
Negative Float32: 1.0

D

void main() {
    import std.stdio, std.math, std.bigint, std.complex;

    writeln("Int:     ", 0 ^^ 0);
    writeln("Ulong:   ", 0UL ^^ 0UL);
    writeln("Float:   ", 0.0f ^^ 0.0f);
    writeln("Double:  ", 0.0 ^^ 0.0);
    writeln("Real:    ", 0.0L ^^ 0.0L);
    writeln("pow:     ", pow(0, 0));
    writeln("BigInt:  ", 0.BigInt ^^ 0);
    writeln("Complex: ", complex(0.0, 0.0) ^^ 0);
}

Output:

Int:     1
Ulong:   1
Float:   1
Double:  1
Real:    1
pow:     1
BigInt:  1
Complex: 1+0i

Dart

import 'dart:math';

void main() {
  var resul = pow(0, 0);
  print("0 ^ 0 = $resul");
}

Output:

0 ^ 0 = 1

Dc

0 0^p

Output:

Delphi

See Pascal.

EasyLang

print pow 0 0

EchoLisp

;; trying the 16 combinations
;; all return the integer 1

(lib 'bigint)
(define zeroes '(integer: 0 inexact=float: 0.000 complex: 0+0i bignum: #0))
(for* ((z1 zeroes) (z2 zeroes)) (write (expt z1 z2)))
    →  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Eiffel

print (0^0)

Output:

Elena

ELENA 6.x

import extensions;
 
public program()
{
    console.printLine("0^0 is ",0.power(0))
}

Output:

0^0 is 0

Elixir

Elixir uses Erlang's :math for power operations and can handle zero to the zero power.

:math.pow(0,0)

Output:

1.0

Emacs Lisp

(expt 0 0)

Output:

EMal

writeLine(0 ** 0) # an integer
writeLine(0.0 ** 0.0) # a real

Output:

1
1.0

ERRE

.....
PRINT(0^0)
.....

Output:

F#

In the REPL:

> let z = 0.**0.;;

val z : float = 1.0

Factor

USING: math.functions.private ; ! ^complex
0 0 ^
C{ 0 0 } C{ 0 0 } ^complex

Output:

--- Data stack:
NAN: 8000000000000
C{ NAN: 8000000000000 NAN: 8000000000000 }

Falcon

VBA/Python programmer's approach not sure if it's the most falconic way

/* created by Aykayayciti Earl Lamont Montgomery
April 9th, 2018 */

x = 0
y = 0
z = x**y
> "z=", z

Output:

z=1
[Finished in 0.2s]

Fermat

0^0

Output:

Forth

0e 0e f** f.

Output:

1.

Of course in an embedded program we would be tempted to "pre-calculate" the answer :-)

: ^0     DROP  1 ;

Output:

0 ^0 . 1 ok

Fortran

program zero
double precision :: i, j
double complex :: z1, z2
i = 0.0D0
j = 0.0D0
z1 = (0.0D0,0.0D0)
z2 = (0.0D0,0.0D0)
write(*,*) 'When integers are used, we have 0^0 = ', 0**0
write(*,*) 'When double precision numbers are used, we have 0.0^0.0 = ', i**j
write(*,*) 'When complex numbers are used, we have (0.0+0.0i)^(0.0+0.0i) = ', z1**z2
end program

Output:

 When integers are used, we have 0^0 =            1
 When double precision numbers are used, we have 0.0^0.0 =    1.0000000000000000     
 When complex numbers are used, we have (0.0+0.0i)^(0.0+0.0i) =  (             NaN,             NaN)

FreeBASIC

' FB 1.05.0 Win64

Print "0 ^ 0 ="; 0 ^ 0
Sleep

Output:

0 ^ 0 = 1

Frink

println[0^0]

Output:

FutureBasic

window 1

print 0^0

HandleEvents

Output:

Gambas

Click this link to run this code

Public Sub Main()

Print 0 ^ 0

End

Output:

GAP

0^0;

Output:

Go

Go does not have an exponentiation operator but has functions in the standard library for three types, float64, complex128, and big.Int. As of Go 1.3, all are documented to return 1.

package main

import (
    "fmt"
    "math"
    "math/big"
    "math/cmplx"
)

func main() {
    fmt.Println("float64:    ", math.Pow(0, 0))
    var b big.Int
    fmt.Println("big integer:", b.Exp(&b, &b, nil))
    fmt.Println("complex:    ", cmplx.Pow(0, 0))
}

Output:

float64:     1
big integer: 1
complex:     (1+0i)

Golfscript

0 0?

Output:

Groovy

Translation of: Java

Test:

println 0**0

Output:

GW-BASIC

PRINT 0^0

Output:

Haskell

import Data.Complex ( Complex((:+)) )

main :: IO ()
main = mapM_ print [
     0 ^ 0,
     0.0 ^ 0,
     0 ^^ 0,
     0 ** 0,
    (0 :+ 0) ^ 0,
    (0 :+ 0) ** (0 :+ 0)
  ]

Output:

1
1.0
1.0
1.0
1.0 :+ 0.0
1.0 :+ 0.0

HolyC

F64 a = 0 ` 0;
Print("0 ` 0 = %5.3f\n", a);

Output:

0 ` 0 = 1.000

Icon and Unicon

"Works" in both languages:

procedure main()
    write(0^0)
end

Output:

->z2z

Run-time error 204
File z2z.icn; Line 2
real overflow, underflow, or division by zero
Traceback:
   main()
   {0 ^ 0} from line 2 in z2z.icn
->

J

   0 ^ 0
1

Note also that this is the multiplicative identity (which means that it's consistent with 1*0 representing 0^1 and with 1*0*0 representing 0^2 and with 1*0*0*0 representing 0^3 and with 1*2*2*2 representing 2^3 and so on. Also, this is the result of finding the product of an empty list:

   */''
1

(In */'' we're finding the product of a list which contains no characters. This is, of course, the same as the product of a list which contains no numbers when both lists contain neither. That said, characters are outside the domain of multiplication in J, so if the list had contained any characters the product would have been an error rather than a result.)

Java

System.out.println(Math.pow(0, 0));

Output:

1.0

JavaScript

Math.pow

Works with: Node.js

In interactive mode:

> Math.pow(0, 0);
1

exponentiation operator (**)

> 0**0
1

jq

Works with: jq version 1.5

Also works with gojq and fq

$ jq -n 'pow(0;0)'
1

It is also worth noting that in jq, gojq, and fq, `pow(0; infinite)` yields 0.

Jsish

puts(Math.pow(0,0));

Output:

Julia

Try all combinations of complex, float, rational, integer and boolean.

using Printf

const types = (Complex, Float64, Rational, Int, Bool)

for Tb in types, Te in types
    zb, ze = zero(Tb), zero(Te)
    r = zb ^ ze
    @printf("%10s ^ %-10s = %7s ^ %-7s = %-12s (%s)\n", Tb, Te, zb, ze, r, typeof(r))
end

Output:

   Complex ^ Complex    = 0 + 0im ^ 0 + 0im = 1.0 + 0.0im  (Complex{Float64})
   Complex ^ Float64    = 0 + 0im ^ 0.0     = 1.0 + 0.0im  (Complex{Float64})
   Complex ^ Rational   = 0 + 0im ^ 0//1    = 1.0 + 0.0im  (Complex{Float64})
   Complex ^ Int64      = 0 + 0im ^ 0       = 1 + 0im      (Complex{Int64})
   Complex ^ Bool       = 0 + 0im ^ false   = 1 + 0im      (Complex{Int64})
   Float64 ^ Complex    =     0.0 ^ 0 + 0im = 1.0 + 0.0im  (Complex{Float64})
   Float64 ^ Float64    =     0.0 ^ 0.0     = 1.0          (Float64)
   Float64 ^ Rational   =     0.0 ^ 0//1    = 1.0          (Float64)
   Float64 ^ Int64      =     0.0 ^ 0       = 1.0          (Float64)
   Float64 ^ Bool       =     0.0 ^ false   = 1.0          (Float64)
  Rational ^ Complex    =    0//1 ^ 0 + 0im = 1.0 + 0.0im  (Complex{Float64})
  Rational ^ Float64    =    0//1 ^ 0.0     = 1.0          (Float64)
  Rational ^ Rational   =    0//1 ^ 0//1    = 1.0          (Float64)
  Rational ^ Int64      =    0//1 ^ 0       = 1//1         (Rational{Int64})
  Rational ^ Bool       =    0//1 ^ false   = 1//1         (Rational{Int64})
     Int64 ^ Complex    =       0 ^ 0 + 0im = 1.0 + 0.0im  (Complex{Float64})
     Int64 ^ Float64    =       0 ^ 0.0     = 1.0          (Float64)
     Int64 ^ Rational   =       0 ^ 0//1    = 1.0          (Float64)
     Int64 ^ Int64      =       0 ^ 0       = 1            (Int64)
     Int64 ^ Bool       =       0 ^ false   = 1            (Int64)
      Bool ^ Complex    =   false ^ 0 + 0im = 1.0 + 0.0im  (Complex{Float64})
      Bool ^ Float64    =   false ^ 0.0     = 1.0          (Float64)
      Bool ^ Rational   =   false ^ 0//1    = 1.0          (Float64)
      Bool ^ Int64      =   false ^ 0       = true         (Bool)
      Bool ^ Bool       =   false ^ false   = true         (Bool)

K

  0^0
1.0

Klingphix

:mypower
    dup not (
      [ drop sign dup 0 equal [ drop 1 ] if ]
      [ power ]
    ) if
;
 
0 0 mypower print nl

"End " input

Output:

1
End

Kotlin

import kotlin.math.pow

fun main() {
   println(0.0.pow(0))
}

Output:

1.0

Lambdatalk

{pow 0 0}
-> 1
{exp 0 0}
-> 1

LDPL

data:
x is number

procedure:
raise 0 to 0 in x
display x lf

Output:

Liberty BASIC

'********
print 0^0
'********

Output:

Locomotive Basic

print 0🠅0

Output:

Lua

No need to try different data types or with / without decimal points as all numbers in Lua are stored in double-precision floating-point format.

print(0^0)

Output:

M2000 Interpreter

M2000 use ** and ^ for power.

Module Checkit {
      x=0
      y=0
      Print x**y=1, x^y=1    ' True True
}
Checkit

Maple

0^0

Output:

However, for consistency with IEEE-754 numerics, we also have a NaN result for the equivalent floating-point exponentiation:

0^0.0

Output:

Float(undefined)

Mathematica/Wolfram Language

0^0

Output:

Indeterminate

MATLAB / Octave

0^0
complex(0,0)^0

Output:

1
1

Maxima

0^0;

Output:

                  0
expt: undefined: 0

Mercury

:- module zero_to_the_zero_power.
:- interface.

:- import_module io.

:- pred main(io::di, io::uo) is det.

:- implementation.

:- import_module float, int, integer, list, string.

main(!IO) :-
   io.format("    int.pow(0, 0) = %d\n", [i(pow(0, 0))], !IO),
   io.format("integer.pow(zero, zero) = %s\n",
        [s(to_string(pow(zero, zero)))], !IO),
   io.format("  float.pow(0.0, 0) = %.1f\n", [f(pow(0.0, 0))], !IO).

:- end_module zero_to_the_zero_power.

Output:

    int.pow(0, 0) = 1
integer.pow(zero, zero) = 1
  float.pow(0.0, 0) = 1.0

Microsoft Small Basic

TextWindow.WriteLine(Math.Power(0,0))

Output:

min

Works with: min version 0.19.3

0 0 pow puts

Output:

1.0

MiniScript

print "The result of zero to the zero power is " + 0^0

Output:

The result of zero to the zero power is 1

МК-61/52

Сx	^	x^y	С/П

The result is error message.

Nanoquery

println 0^0

Output:

Neko

Neko uses the C math library for exponentiation, Zero to the zero in math.pow(x, y) is treated as being 1.

/**
 Zero to the zeroth power, in Neko
*/

var math_pow = $loader.loadprim("std@math_pow", 2)

$print(math_pow(0, 0), "\n")

Output:

prompt$ nekoc zero-to-the-zero.neko
prompt$ neko zero-to-the-zero.n
1

NetRexx

x=0
Say '0**0='||x**x

Output:

0**0=1

NewLISP

(pow 0 0)

Output:

Nial

Create an exponentiation table for all type combinations (of integer 0, float 0.0 and boolean o):

     0 0.0 o outer power 0 0.0 o
+--+--+--+
| 1|1.| 1|
+--+--+--+
|1.|1.|1.|
+--+--+--+
| 1|1.| 1|
+--+--+--+

Nim

import math

echo pow(0.0, 0.0)  # Floating point exponentiation.
echo 0 ^ 0          # Integer exponentiation.

Output:

1.0
1

OCaml

In the interpreter:

# 0.0 ** 0.0;;
- : float = 1.
# Complex.pow Complex.zero Complex.zero;;
- : Complex.t = {Complex.re = nan; Complex.im = nan}
# #load "nums.cma";;
# open Num;;
# Int 0 **/ Int 0;;                 
- : Num.num = Int 1

Oforth

0 0 pow println

Output:

Ol

(print "0^0: " (expt 0 0))
(print "0.0^0: " (expt (inexact 0) 0))

Output:

0^0: 1
0.0^0: 1

ooRexx

/**********************************************************************
* 21.04.2014 Walter Pachl
**********************************************************************/
Say 'rxCalcpower(0,0)  ->' rxCalcpower(0,0)
Say '0**0              ->' 0**0
::requires rxmath library

Output:

rxCalcpower(0,0)  -> 1
0**0              -> 1

Openscad

echo (0^0);

PARI/GP

0 raised to the power of exact 0 is 1, but 0 cannot be raised to the power of an inexact 0:

0^0
0.^0
0^0.

Output:

%1 = 1
%2 = 1
  ***   at top-level: 0^0.
  ***                   ^---
  *** _^_: domain error in gpow(0,n): n <= 0
  ***   Break loop: type 'break' to go back to GP prompt

Pascal

Works with: Free Pascal

Library: math

program ZToZ;
uses
  math;
begin
  write('0.0 ^ 0 :',IntPower(0.0,0):4:2);
  writeln('   0.0 ^ 0.0 :',Power(0.0,0.0):4:2);
end.

output

0.0 ^ 0 :1.00   0.0 ^ 0.0 :1.00

Perl

print 0 ** 0, "\n";

use Math::Complex;

print cplx(0,0) ** cplx(0,0), "\n";

Output:

1
1

Phix

Library: Phix/basics

?power(0,0)
requires("0.8.4") -- (now fixed/crashes on earlier versions)
include complex.e
complex a = complex_new(0,0),
        b = complex_power(a,a)
string sa = complex_sprint(a,true),
       sb = complex_sprint(b,true)
printf(1,"%s ^ %s = %s\n",{sa,sa,sb})

Output:

1
0+0i ^ 0+0i = 1+0i

Phixmonti

def mypower
    dup not if
        . sign dup 0 == if . 1 endif
    else
        power
    endif
enddef

0 0 mypower print

Output:

PHP

<?php
echo pow(0,0);
echo 0 ** 0; // PHP 5.6+ only
?>

Output:

1
1

PicoLisp

 
(** 0 0)

Output:

1

Pike

write( pow(0, 0) +"\n" );

Output:

PL/I

 zhz: Proc Options(Main);
 Dcl a dec float(10) Init(1);
 Dcl b dec float(10) Init(0);
 Put skip list('1**0=',a**b);
 Put skip list('0**1=',b**a);
 Put skip list('0**0=',b**b);
 End;

Output:

1**0=                    1.000000000E+0000
0**1=                    0.000000000E+0000
0**0=
IBM0682I  ONCODE=1553  X in EXPONENT(X) was invalid.
   At offset +0000025B in procedure with entry ZHZ

Plain English

To run:
Start up.
Put 0 into a number.
Raise the number to 0.
Convert the number to a string.
Write the string to the console.
Wait for the escape key.
Shut down.

Output:

PowerShell

Write-Host "0 ^ 0 = " ([math]::pow(0,0))

Output :

0 ^ 0 =  1

PureBasic

If OpenConsole()
  PrintN("Zero to the zero power is " + Pow(0,0))
  PrintN("")
  PrintN("Press any key to close the console")
  Repeat: Delay(10) : Until Inkey() <> ""
  CloseConsole()
EndIf

Output:

Zero to the zero power is 1

Pyret

num-expt(0, 0)

Output:

1

Python

Python3

from decimal import Decimal
from fractions import Fraction
from itertools import product

zeroes = [0, 0.0, 0j, Decimal(0), Fraction(0, 1), -0.0, -0.0j, Decimal(-0.0)]
for i, j in product(zeroes, repeat=2):
    try:
        ans = i**j
    except:
        ans = '<Exception raised>'
    print(f'{i!r:>15} ** {j!r:<15} = {ans!r}')

Output:

              0 ** 0               = 1
              0 ** 0.0             = 1.0
              0 ** 0j              = (1+0j)
              0 ** Decimal('0')    = '<Exception raised>'
              0 ** Fraction(0, 1)  = 1
              0 ** -0.0            = 1.0
              0 ** (-0-0j)         = (1+0j)
              0 ** Decimal('-0')   = '<Exception raised>'
            0.0 ** 0               = 1.0
            0.0 ** 0.0             = 1.0
            0.0 ** 0j              = (1+0j)
            0.0 ** Decimal('0')    = '<Exception raised>'
            0.0 ** Fraction(0, 1)  = 1.0
            0.0 ** -0.0            = 1.0
            0.0 ** (-0-0j)         = (1+0j)
            0.0 ** Decimal('-0')   = '<Exception raised>'
             0j ** 0               = (1+0j)
             0j ** 0.0             = (1+0j)
             0j ** 0j              = (1+0j)
             0j ** Decimal('0')    = '<Exception raised>'
             0j ** Fraction(0, 1)  = (1+0j)
             0j ** -0.0            = (1+0j)
             0j ** (-0-0j)         = (1+0j)
             0j ** Decimal('-0')   = '<Exception raised>'
   Decimal('0') ** 0               = '<Exception raised>'
   Decimal('0') ** 0.0             = '<Exception raised>'
   Decimal('0') ** 0j              = '<Exception raised>'
   Decimal('0') ** Decimal('0')    = '<Exception raised>'
   Decimal('0') ** Fraction(0, 1)  = '<Exception raised>'
   Decimal('0') ** -0.0            = '<Exception raised>'
   Decimal('0') ** (-0-0j)         = '<Exception raised>'
   Decimal('0') ** Decimal('-0')   = '<Exception raised>'
 Fraction(0, 1) ** 0               = Fraction(1, 1)
 Fraction(0, 1) ** 0.0             = 1.0
 Fraction(0, 1) ** 0j              = (1+0j)
 Fraction(0, 1) ** Decimal('0')    = '<Exception raised>'
 Fraction(0, 1) ** Fraction(0, 1)  = Fraction(1, 1)
 Fraction(0, 1) ** -0.0            = 1.0
 Fraction(0, 1) ** (-0-0j)         = (1+0j)
 Fraction(0, 1) ** Decimal('-0')   = '<Exception raised>'
           -0.0 ** 0               = 1.0
           -0.0 ** 0.0             = 1.0
           -0.0 ** 0j              = (1+0j)
           -0.0 ** Decimal('0')    = '<Exception raised>'
           -0.0 ** Fraction(0, 1)  = 1.0
           -0.0 ** -0.0            = 1.0
           -0.0 ** (-0-0j)         = (1+0j)
           -0.0 ** Decimal('-0')   = '<Exception raised>'
        (-0-0j) ** 0               = (1+0j)
        (-0-0j) ** 0.0             = (1+0j)
        (-0-0j) ** 0j              = (1+0j)
        (-0-0j) ** Decimal('0')    = '<Exception raised>'
        (-0-0j) ** Fraction(0, 1)  = (1+0j)
        (-0-0j) ** -0.0            = (1+0j)
        (-0-0j) ** (-0-0j)         = (1+0j)
        (-0-0j) ** Decimal('-0')   = '<Exception raised>'
  Decimal('-0') ** 0               = '<Exception raised>'
  Decimal('-0') ** 0.0             = '<Exception raised>'
  Decimal('-0') ** 0j              = '<Exception raised>'
  Decimal('-0') ** Decimal('0')    = '<Exception raised>'
  Decimal('-0') ** Fraction(0, 1)  = '<Exception raised>'
  Decimal('-0') ** -0.0            = '<Exception raised>'
  Decimal('-0') ** (-0-0j)         = '<Exception raised>'
  Decimal('-0') ** Decimal('-0')   = '<Exception raised>'

Python2

from decimal import Decimal
from fractions import Fraction
for n in (Decimal(0), Fraction(0, 1), complex(0), float(0), int(0)):
	try:
		n1 = n**n
	except:
		n1 = '<Raised exception>'
	try:
		n2 = pow(n, n)
	except:
		n2 = '<Raised exception>'
	print('%8s: ** -> %r; pow -> %r' % (n.__class__.__name__, n1, n2))

Output:

 Decimal: ** -> '<Raised exception>'; pow -> '<Raised exception>'
Fraction: ** -> Fraction(1, 1); pow -> Fraction(1, 1)
 complex: ** -> (1+0j); pow -> (1+0j)
   float: ** -> 1.0; pow -> 1.0
     int: ** -> 1; pow -> 1

QB64

Print 0 ^ 0

Output:

Alternatively:

i% = 0 'Integer
l& = 0 'Long integer
s! = 0.0 'Single precision floating point
d# = 0.0 'Double precision floating point
b` = 0 '_Bit
bb%% = 0 '_Byte
isf&& = 0 '_Integer64

Print i% ^ i%
Print l& ^ l&
Print s! ^ s!
Print d# ^ d#
Print b` ^ b`
Print bb%% ^ bb%%
Print isf&& ^ isf&&

Output:

NB: Values with 0 decimals are trimmed by Print's casting from number value to String.

Quackery

As a dialogue in the Quackery shell.

/O> 0 0 **
... 

Stack: 1

R

print(0^0)

Output:

Racket

#lang racket
;; as many zeros as I can think of...
(define zeros (list
               0  ; unspecified number type
               0. ; hinted as float
               #e0 ; explicitly exact
               #i0 ; explicitly inexact
               0+0i ; exact complex
               0.+0.i ; float inexact
               ))
(for*((z zeros) (p zeros))
  (printf "(~a)^(~a) = ~s~%" z p
  (with-handlers [(exn:fail:contract:divide-by-zero? exn-message)]
    (expt z p))))

Output:

(0)^(0) = 1
(0)^(0.0) = 1.0
(0)^(0) = 1
(0)^(0.0) = 1.0
(0)^(0) = 1
(0)^(0.0+0.0i) = "expt: undefined for 0 and 0.0+0.0i"
(0.0)^(0) = 1
(0.0)^(0.0) = 1.0
(0.0)^(0) = 1
(0.0)^(0.0) = 1.0
(0.0)^(0) = 1
(0.0)^(0.0+0.0i) = +nan.0+nan.0i
(0)^(0) = 1
(0)^(0.0) = 1.0
(0)^(0) = 1
(0)^(0.0) = 1.0
(0)^(0) = 1
(0)^(0.0+0.0i) = "expt: undefined for 0 and 0.0+0.0i"
(0.0)^(0) = 1
(0.0)^(0.0) = 1.0
(0.0)^(0) = 1
(0.0)^(0.0) = 1.0
(0.0)^(0) = 1
(0.0)^(0.0+0.0i) = +nan.0+nan.0i
(0)^(0) = 1
(0)^(0.0) = 1.0
(0)^(0) = 1
(0)^(0.0) = 1.0
(0)^(0) = 1
(0)^(0.0+0.0i) = "expt: undefined for 0 and 0.0+0.0i"
(0.0+0.0i)^(0) = 1
(0.0+0.0i)^(0.0) = 1.0+0.0i
(0.0+0.0i)^(0) = 1
(0.0+0.0i)^(0.0) = 1.0+0.0i
(0.0+0.0i)^(0) = 1
(0.0+0.0i)^(0.0+0.0i) = +nan.0+nan.0i

Raku

(formerly Perl 6)

Works with: Rakudo version 2018.03

say '    type         n      n**n  exp(n,n)';
say '--------  --------  --------  --------';

for 0, 0.0, FatRat.new(0), 0e0, 0+0i {
    printf "%8s  %8s  %8s  %8s\n", .^name, $_, $_**$_, exp($_,$_);
}

Output:

    type         n      n**n  exp(n,n)
--------  --------  --------  --------
     Int         0         1         1
     Rat         0         1         1
  FatRat         0         1         1
     Num         0         1         1
 Complex      0+0i      1+0i      1+0i

Red

Shown using the operator, the function, and the math mini-DSL that uses the order of operations from mathematics:

Red[]
print 0 ** 0
print power 0 0
print math [0 ** 0]

Output:

1
1
1

Relation

echo pow(0,0)
// 1

REXX

/*REXX program shows the results of  raising zero  to the  zeroth power.*/
say  '0 ** 0  (zero to the zeroth power) ───► '    0**0

using PC/REXX
using Personal REXX
using REGINA
using ooRexx

Output:

0 ** 0  (zero to the zeroth power) ───►  1

using R4

Output:

Error 26 : Invalid whole number (SYNTAX)
Information: 0 ** 0 is undefined
Error occurred in statement# 2
Statement source: say '0 ** 0  (zero to the zeroth power) ───► ' 0**0
Statement context: C:\ZERO_TO0.REX, procedure: ZERO_TO0

using ROO

Output:

Error 26 : Invalid whole number (SYNTAX)
Information: 0 ** 0 is undefined
Error occurred in statement# 2
Statement source: say '0 ** 0  (zero to the zeroth power) ───► ' 0**0
Statement context: C:\ZERO_TO0.REX, procedure: ZERO_TO0

Ring

x = 0
y = 0
z = pow(x,y)
see "z=" + z + nl   # z=1

RPL

0 0 ^

Output for HP-48G and older models

1: 1

Output for HP-49 and newer models

1: ?

Ruby

require 'bigdecimal'

[0, 0.0, Complex(0), Rational(0), BigDecimal("0")].each do |n|
  printf "%10s: ** -> %s\n" % [n.class, n**n]
end

Output:

   Integer: ** -> 1
     Float: ** -> 1.0
   Complex: ** -> 1+0i
  Rational: ** -> 1/1
BigDecimal: ** -> 0.1e1

Rust

fn main() {
    println!("{}",0u32.pow(0));
}

Output:

S-lang

print(0^0);

Output:

1.0

Scala

Library: Scala

  assert(math.pow(0, 0) == 1, "Scala blunder, should go back to school !")

Scheme

(display (expt 0 0)) (newline)
(display (expt 0.0 0.0)) (newline)
(display (expt 0+0i 0+0i)) (newline)

Output:

1
1.0
1.0

Seed7

$ include "seed7_05.s7i";
  include "float.s7i";
  include "complex.s7i";

const proc: main is func
  begin
    writeln("0      ** 0   = " <& 0 ** 0);
    writeln("0.0    ** 0   = " <& 0.0 ** 0);
    writeln("0.0    ** 0.0 = " <& 0.0 ** 0.0);
    writeln("0.0+0i ** 0   = " <& complex(0.0) ** 0);
  end func;

Output:

0      ** 0   = 1
0.0    ** 0   = 1.0
0.0    ** 0.0 = 1.0
0.0+0i ** 0   = 1.0+0.0i

SenseTalk

set a to 0
set b to 0

put a to the power of b
// Prints: 1

Sidef

[0, Complex(0, 0)].each {|n|
    say n**n
}

Output:

1
1

Taking the 0'th root of a number and raising it back to the zero power, we also get a 1:

say 0.root(0).pow(0)       # => 1
say ((0**(1/0))**0)        # => 1

Sinclair ZX81 BASIC

PRINT 0**0

Output:

Smalltalk

0 raisedTo: 0 
0.0 raisedTo: 0.0

Output:

1
1.0

smart BASIC

PRINT 0^0

Output:

SNOBOL4

	OUTPUT = (0 ** 0)
END

SQL

SQL> select power(0,0) from dual;

Output:

POWER(0,0)
----------
         1

Standard ML

In the interpreter:

- Math.pow (0.0, 0.0);
val it = 1.0 : real

Stata

. display 0^0
1

Swift

import Darwin
print(pow(0.0,0.0))

Output:

1.0

Symsyn

 (0^0) []

Output:

Tcl

Interactively…

% expr 0**0
1
% expr 0.0**0.0
1.0

TI SR-56

0 Yx 0 =

Output:

TI-83_BASIC

0^0

Output:

ERROR:DOMAIN

uBasic/4tH

Print 0^0

Output:

1

0 OK, 0:9

Ursa

Cygnus/X Ursa is written in Java, and as a result returns 1.0 when raising 0 to the 0.

> out (pow 0 0) endl console
1.0

VBA

Public Sub zero()
    x = 0
    y = 0
    z = 0 ^ 0
    Debug.Print "z ="; z
End Sub

Output:

z = 1

VBScript

WScript.Echo 0 ^ 0

Output:

Verilog

module main;
  initial begin
    $display("0 ^ 0 = ", 0**0);
    $finish ;
  end
endmodule

Output:

0 ^ 0 =           1

Visual Basic .NET

Module Program
    Sub Main()
        Console.Write(0^0)
    End Sub
End Module

Output:

V (Vlang)

// Zero to the zero power, in V
// Tectonics: v run zero-to-the-zero-power.v
module main
import math

// starts here
// V does not include an exponentiation operator, but uses a math module
pub fn main() {
    println(math.pow(0, 0))
}

Output:

prompt$ v run rosetta/zero-to-the-zero-power.v
1.

Wren

System.print(0.pow(0))

Output:

XLISP

XLISP 3.3, September 6, 2002 Copyright (c) 1984-2002, by David Betz
[1] (expt 0 0)

1
[2]

XPL0

RlOut(0, Pow(0., 0.))

Output:

    1.00000

Zig

const std = @import("std");

pub fn main() !void {
    const stdout = std.io.getStdOut().writer();
    try stdout.print("0^0 = {d:.8}\n", .{std.math.pow(f32, 0, 0)});
}

Output:

0^0 = 1.00000000

zkl

(0.0).pow(0)  //--> 1.0
var BN=Import("zklBigNum"); // big ints
BN(0).pow(0) //--> 1