Discussion:  All Topics 
Topic:  exponents 
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Subject:  RE: exponents 
Author:  Alan Cooper 
Date:  Oct 18 2004 
> Is it
(the fact that powers with negative exponents
are the reciprocals of the ones with positive exponents)
> not simply a result of the same empirical rule a^5/a^3 =
> a^(53), and so it follows for completion that a^3/a^5 = a^(35),
> and likewise a^n/a^n = a^0 ?
It is certainly the most natural definition (and probably the only reasonable
one), but not the only possible one. My point was just that it is still a
definition (which we choose) rather than a fact of the kind that we have no
choice about (such as a theorem  which is an unavoidable consequence of what we
have already chosen). And I worry that by not making the distinction we may
leave some students feeling frustrated at their failure to see as obvious
something that is not even strictly true(in the sense that they may be
interpreting it).
Alan
 
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