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Thanks for pointing that out, Walter. Interestingly, Quattro Pro says
that -2^2 is -4, while Excel (as you say) computes -2^2 as +4.
My first reaction was that you were squaring a negative number, but
on looking at it again, the precedence of arithmetical operations says
that exponents are always computed first. Excel is wrong.
----- Original Message -----
From: "W Lake" <wlake@xxxxxxxxx>
To: <metastock@xxxxxxxxxxxxx>
Sent: Wednesday, September 19, 2001 8:08 PM
Subject: Exponents and negative numbers
> I have checked Mathematica, MathCAD and Derive. All three say
> that -2^2 = -4, that -2^4 = -16 and that all of the data points from any
> series, say out to -2^64 are on a negative power curve.
>
> There is no mention of using brackets or any special "input" techniques to
> handle negative numbers.
>
> Attached is an explanation of why -3^2 = -9 from a web site. If the
> explanation is correct, then Excel (-2^2 = 4) is wrong and I need to rethink
> my usage.
>
> Can anyone add to or refute the logic given in the emails below.
>
> Walter
>
> =============================================
>
> Exponents and Negative numbers
>
> Date: 03/02/97 at 11:15:14
> From: Anonymous
> Subject: Exponents and negative numbers
>
> Dear Dr. Math,
>
> In different texts about this same question, I can find two different
> answers. The solution to: (-3)squared = 9. But when -3 is squared
> (without the brackets), one source may say 9 while another source
> says -9.
>
> In context, the -3 squared used in sequence will always be -9; why
> would the exponent apply to the negative sign unless it is enclosed
> by a sign of grouping? In short, why wouldn't the answer to -3
> squared, standing alone and without parenthesis or brackets, be -9?
>
> Thanks very much.
>
> Sincerely,
> Marvin E. Crim
>
>
> ----------------------------------------------------------------------------
> ----
>
>
> Date: 03/09/97 at 14:53:39
> From: Doctor Ken
> Subject: Re: exponents and negative numbers
>
> Hi Marvin -
>
> After a lengthy discussion among the Drs. Math to make sure we had our
> facts straight, I think we have an answer for you.
>
> If you ever see the expression -3^2 evaluated as 9, that's incorrect.
> The exponentiation is always done before the negation unless there are
> parentheses there to indicate otherwise.
>
> However, there are some contexts in which it _looks_ like texts are
> saying that -3^2 = 9, but a closer inspection will either reveal a
> subtle interpretation or a misunderstanding. For instance, what is the
> difference between the following statements:
>
> "If I take negative three and square it, I get nine."
> "If I square negative three, I get nine."
> "If I evaluate negative three squared, I get negative nine."
> "If I take the opposite of three squared, I get negative nine."
>
> All of the above statements are correct. The reason some of them
> end up with 9 as the answer and some end up with -9 is that some of
> the statements have groupings implied in their phrasing. The first
> two statements translate into algebraic notation as (-3)^2 = 9, the
> third statement translates to -3^2 = -9, and the fourth statement
> translates to -(3^2) = -9.
>
> So the confusion here is not really about mathematical notation, it's
> about how to translate English into mathematical notation. Either
> that, or your textbook is incorrect!
>
> I hope we've cleared up some confusion. The bottom line is that
> -a^b is always evaluated as -(a^b).
>
> -Doctor Ken, The Math Forum
> Check out our web site! http://forum.swarthmore.edu/dr.math/
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