Fractional ExponentsDate: 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 Check out our web site! http://mathforum.org/dr.math/ |
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