Fractional Exponents

Date: 08/09/97 at 00:41:55
From: Anonymous
Subject: Fractional exponents

I am a middle school teacher and cannot show a proof to my kids why X^
1/2 is equal to the square root of X. Is there actually a proof, or is 
it just a mathematical convention we use?  

Tom Schmidt   

Date: 08/09/97 at 06:48:01
From: Doctor Anthony
Subject: Re: Fractional exponents

You use the normal rules of indices.  We have  (x^a)(x^b) = x^(a+b)

  so   x^(1/2).x^(1/2) = x^(1/2 + 1/2) = x^(1)  =  x

But by definition  sqrt(x)*sqrt(x) = x

Comparing the two equations  x^(1/2) = sqrt(x)

-Doctor Anthony,  The Math Forum
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