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Topic: evaluating -x^c
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Subject:   RE: evaluating -x^c
Author: Alan Cooper
Date: Sep 27 2004
On Sep 27 2004, Bethany wrote:
> . . . 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 1-x^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.)


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