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 March 2nd, 2012, 05:21 AM #1 Newbie   Joined: Mar 2012 Posts: 4 Thanks: 0 Exponent X to the power 0 =1 prove it
 March 2nd, 2012, 06:13 AM #2 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: Exponent Assume the conclusion. Q.E.D. Seriously, though. You prove it! And what if x = 0?
March 2nd, 2012, 06:35 AM   #3
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
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Re: Exponent

Hello, Thinkhigh!

What "facts" are we allowed to assume?

Quote:
 $\text{Prove: }\:x^0 \:=\:1$

If we can assume the Rules of Exponents, there is a proof.

$\text{First, assume }x\,\ne\,0.$

$\text{From the Rules of Exponents: }\:\frac{x^3}{x^3} \:=\:x^{3-3}\;\;\;\Rightarrow\;\;\;\frac{x^3}{x^3} \:=\:x^0\;\;[1]$

$\text{W\!e know: }\:\frac{x^3}{x^3} \:=\:1\;\;[2]
\;\;\;\text{A nonzero number divided by itself equals 1.}$

$\text{Equate [1] and [2]: }\:x^0 \:=\:1$

 March 2nd, 2012, 06:42 AM #4 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: Exponent Soroban and I have been working on our "good cop, bad cop" routine for a while. One of these days, maybe I'll get promoted to "good cop"!

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