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Topic: Please remind me why -3^2 = -9
Replies: 26   Last Post: Nov 18, 2012 7:51 PM

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Guy Brandenburg

Posts: 81
Registered: 1/30/05
Re: Please remind me why -3^2 = -9
Posted: Oct 18, 2012 7:04 AM
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att1.html (3.9 K)

It's a convention. In a case like that, one really ought to use parentheses to make the meaning clear, since a lot of people, not just youngsters, will get confused.

If one intends to say (-3)*(-3), then write (-3)^2. If one means - (3)*(3), then write - (3^2).

Writing -3^2 is simply asking for confusion.
 
Guy Brandenburg, Washington, DC 
http://gfbrandenburg.wordpress.com/
http://home.earthlink.net/~gfbranden/GFB_Home_Page.html
============================


________________________________
From: "john.peterson20@comcast.net" <john.peterson20@comcast.net>
To: Philip Mahler <mahlerp@middlesex.mass.edu>
Cc: mathedcc <mathedcc@mathforum.org>
Sent: Thursday, October 18, 2012 6:05 AM
Subject: Re: Please remind me why -3^2 = -9


Phil,

-3 means -1 x 3, so -3^2 is (-1)(3^2) = (-1)(9) = -9.


John Peterson



________________________________
From: "Philip Mahler" <mahlerp@middlesex.mass.edu>
To: "mathedcc" <mathedcc@mathforum.org>
Sent: Thursday, October 18, 2012 5:37:07 AM
Subject: Please remind me why -3^2 = -9

Please remind me why -3^2 = -9 I have been teaching a long time, and I know from experience that 50% of students will tell me that ?3^2 = +9 on a test or a final, despite having discussed it a few times in a course.

When I first started teaching I taught calculus and precalc. Piece of cake. Then I started with an Algebra I class and couldn?t connect at all for the first week or so. I was ready to believe I couldn?t teach. I simply could not explain how I got the right answers when evaluating expressions... Then I discovered the order of operations (PEMDAS to some). A definition of the order of operations which I had so internalized that I didn?t know there was a rule for it. Since that discovery I?ve been a wonderful teacher. :-)

So... I must be missing something that so many of my students think ?3^2 is +9. What is the rule I have never discovered?

Full disclosure: I think ?k^2, k a constant, should be banned from mathematics texts and tests. -x^2, x a variable, evaluated for say ?3, absolutely (no pun intended) but not ?3^2.

Phil


Date Subject Author
10/18/12
Read Please remind me why -3^2 = -9
Phil Mahler
10/18/12
Read Re: Please remind me why -3^2 = -9
John Peterson
10/18/12
Read Re: Please remind me why -3^2 = -9
Guy Brandenburg
10/18/12
Read RE: Please remind me why -3^2 = -9
Wayne Mackey
10/18/12
Read RE: Please remind me why -3^2 = -9
Phil Mahler
10/18/12
Read RE: Please remind me why -3^2 = -9
RotmanJ
10/18/12
Read Re: Please remind me why -3^2 = -9
Paul Hertzel
10/18/12
Read Re: Please remind me why -3^2 = -9
Phil Mahler
10/18/12
Read Re: Please remind me why -3^2 = -9
Clyde Greeno
10/19/12
Read Re: Please remind me why -3^2 = -9
Clyde Greeno
10/19/12
Read Re: Please remind me why -3^2 = -9
Alain Schremmer
10/19/12
Read RE: Please remind me why -3^2 = -9
Wayne Mackey
10/19/12
Read Re: Please remind me why -3^2 = -9
Alain Schremmer
10/19/12
Read Re: Please remind me why -3^2 = -9
Clyde Greeno
10/19/12
Read Re: Please remind me why -3^2 = -9
Alain Schremmer
10/21/12
Read RE: Please remind me why -3^2 = -9
Wayne Mackey
11/14/12
Read Re: Please remind me why -3^2 = -9
Beth Hentges
11/15/12
Read Re: Please remind me why -3^2 = -9
Clyde Greeno
11/16/12
Read Re: Please remind me why -3^2 = -9
Alain Schremmer
10/18/12
Read RE: Please remind me why -3^2 = -9
Collinge, Peter (Mathematics)
10/18/12
Read Re: Please remind me why -3^2 = -9
Guy Brandenburg
10/18/12
Read Re: Please remind me why -3^2 = -9
Phil Mahler
10/18/12
Read Re: Please remind me why -3^2 = -9
Alain Schremmer
11/18/12
Read Re: Please remind me why -3^2 = -9
EddieC
11/18/12
Read RE: Please remind me why -3^2 = -9
Matthews, George
11/18/12
Read Re: Please remind me why -3^2 = -9
Phil Mahler
11/18/12
Read Re: Please remind me why -3^2 = -9
Alain Schremmer

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