RE: [xmca] Why Does N to the Power of Zero = 1?

["David H Kirshner" <dkirsh@lsu.edu>]

David,

It's defined the way it is so that exponent relations are maintained in a consistent way. 
For instance if we take powers of 3 using the usual definition of repeated multiplication, we have a pattern whereby each lesser power is the previous one divided by the base:

3^4 = 3x3x3x3 = 81
3^3 = 3x3x3 = 27 = 3^4 / 3
3^2 = 3x3 = 9 = 3^3 / 3
3^1 = 3 = 3^2 / 3, so 
3^0 = ? = 3^1 / 3 = 1

The same pattern explains how negative exponents are defined. 

I hope the traffic clears soon. 

David


-----Original Message-----
From: xmca-bounces@weber.ucsd.edu [mailto:xmca-bounces@weber.ucsd.edu] On Behalf Of David Kellogg
Sent: Monday, February 28, 2011 12:42 AM
To: xmca
Subject: [xmca] Why Does N to the Power of Zero = 1?

I've been working on math games to play in the back seat of a car while stuck in a Korean traffic jam (during the various lunar holidays when everybody visits the ancestral graves).
 
So I've got a version of "Twenty Four" with cell phone numbers called "Cell Phone Golf". In Korea, cell phone numbers usually have eight digits once you remove the company code. Mine, for example is 3475 2505.
 
For the first hole of cell phone golf we split my number in two. My young opponent takes 3475 and I take 2505. We both work to hit the number ONE using the four arithmetic operations (and then two, and so on all the way up to eighteen, or until the traffic clears up). My opponent tees off first, 
 
(3-4) + (7-5) = 1
 
Man, she's got a mean drive. Just look at those negative numbers. A hole in one! 
 
Now it's my turn. This is going to be hard to beat.
 
(2-5) + (0+5). Nah. that doesn't work....
 
I've got it! 
 
(2 + 5 + 5) RAISED to the POWER of ZERO!
 
A hole in one! Ha! I explain to my young opponent that any number raised to the power of zero is 1.
 
But she gives me a skeptical sidelong glance: I am suspected of cheating. She demands to know WHY any number raised to the power of zero is equal to one. 
 
Can anyone help me out before the traffic improves?
 
David Kellogg
Seoul National University of Education
 
 


      
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