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Topic: evaluating -x^c

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Subject:   RE: evaluating -x^c
Author: Craig
Date: Sep 27 2004
This is a good problem for teaching order of operations.  Many textbooks teach
PEMDAS... parentheses (grouping), exponents, multiplication and division from
left to right, and addition and subtraction from left to right.  Where does
negation fit into this scheme?  Well, negation is multiplication by negative
one, so negation comes AFTER exponents.  Thus, -x^c is the negation of x^c, or
-x^c = -(x^c).  

When you write 3.8 instead of x, the meaning of -3.8 becomes unclear--do you
mean the number -3.8, or the negation of the number 3.8?  The TI-83 is
consistent in handling it as the negation: your example of -3.8^2.1 is handled
as the negation of 3.8^2.1, which is perfectly well defined.  But, when you try
graphing x^2.1, at x=-3.8 the calculator is trying to compute (-3.8)^2.1,
which is NOT defined (because, after all, you can't take the tenth root of a
negative number...).

With Excel, "negation" per se doesn't work as expected.  The negative sign is
assumed to be part of the number, even if the number is treated as a variable.
This, I believe, is a programming fault, because it is inconsistent.  For
example, I put 3.8 in cell A1, then =-A1 in A2, and got -3.8.  When I
changed A1 to be -3.8, then A2 became 3.8, which is --3.8, which I as a math
teacher would take to mean the negation of (-3.8).

Bottom line: at least for my thinking on order of operations, the TI-83
handles the problem correctly, provided you think of the (-) key as a negation
key; Excel handles the problem incorrectly.

Any other ideas on order of operations?

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