Discussion:  Traffic Jam Applet tool 
Topic:  evaluating x^c 
Related Item:  http://mathforum.org/mathtools/tool/10/ 
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Subject:  RE: evaluating x^c 
Author:  Alan Cooper 
Date:  Sep 27 2004 
> . . . if I type in the expression 3.8^2.1 I get a response to
> be 16.502... Yet when I try to graph x^2.1 the graph is only
> defined for positive x. . .
These are not inconsistent, and both are correct.
By the standard "order of operations" convention, powers precede multiplication
and x is interpreted as (1)x.
This interpretation is necessary since otherwise 1x^2 becomes ambiguous.
So 3.8^2.1=(1)((3.8)^(2.1)) which exists and is negative.
But at x=3.8, x^(2.1)=(3.8)^(2.1) which is undefined (or at least not
real)because it is a fractional power of a negative number.
(By the way my browser "helpfully" turned your correct text into an error by
making you say, in effect, that (3.8)^(2).1 is undefined)
> Also of interest to note is in MS Excel, typing that
> expression yields an error.
I would like to say that Microsoft's error message is itself an error, but there
may be some excuse.
In fact, to interpret x^c as (x)^c *is* unacceptable because of the
ambiguity I mentioned above, but some calculators and texts do introduce a
separate symbol for the "unary minus" (sometimes with a superscript minus sign
or a different color). If the unary minus symbol cannot be used in any other
way, and is easy to distinguish from the subtraction operator (which I doubt)
then the brackets on the "x" could be dropped without ambiguity. (So before
accusing MS I guess I should take a close look at that minus sign.)
cheers,
Alan
 
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