A simple math question regarding exponents--

[distancia]

and I cannot find this rule written ANYWHERE! but I know for a fact it exists. Why is it not clearly stated in any of the books I have seen? Only one place--in the MathUSee Pre-algebra video and Teacher Manual, does it even hint at how to solve this.

 

But nowhere else have I seen it explained.

 

-3 ^2= -9

 

-(3)^2= -9

 

(-3)^2= 9

 

Why is the first example not a positive? And where is it written in the "rules" of exponents / Algebra?

 

Thanks!

Edited October 18, 2010 by distancia

[Heather in VA]

-3^2 = -9 because of the - is technically -1 times 3 and since you do exponents first (PEMDAS) you do 3^2 and then multiply that answer (9) by -1 which equals -9.

 

Heather

[Julie of KY]

and I cannot find this rule written ANYWHERE! but I know for a fact it exists. Why is it not clearly stated in any of the books I have seen? Only one place--in the MathUSee Pre-algebra video and Teacher Manual, does it even hint at how to solve this.

 

But nowhere else have I seen it explained.

 

-3 ^2= -9

 

-(3)^2= -9

 

(-3)^2= 9

 

Why is the first example not a positive? And where is it written in the "rules" of exponents / Algebra?

 

Thanks!

 

The first one is negative because it is the same as -(3^2).

The negative in front of the coefficient is only raised to the exponent if it is within the parentheses as in the third example.

[HollyDay]

and I cannot find this rule written ANYWHERE! but I know for a fact it exists. Why is it not clearly stated in any of the books I have seen? Only one place--in the MathUSee Pre-algebra video and Teacher Manual, does it even hint at how to solve this.

 

But nowhere else have I seen it explained.

 

-3 ^2= -9

 

-(3)^2= -9

 

(-3)^2= 9

 

Why is the first example not a positive? And where is it written in the "rules" of exponents / Algebra?

 

Thanks!

 

This drove me nuts too. Saxon actually does a pretty good job explaining this one.

 

In the first example, only the 3 is raised to the power. It is "the opposite of positive 3 raised to the 2nd power" So, positive 3 to the 2nd power is 9. Now, that the exponent is simplified, you include the negative symbol making it negative 9.

 

The second example is the same process and read the same way, but I think it is easier to see. The negative symbol is outside the () so it is separate. I think it is clearer because the negative symbol is removed from the number by the ().

 

In the last example, the negative is included in the power because it is inside the symbol of inclusion (). So it is read negative 3 elevated to the second power, which is positive 9 (-3 times -3 = 9).

 

Is that any clearer or is it still muddy? For a while my dc would use () to help her see the situation more clearly even if they were not there originally.

[distancia]

Okay, now you ladies have told me this: where have you seen it actually written? My sweet sunshine DD :mad: likes to see it in writing. Hearing it from another source--even a teacher--doesn't cut it. I cannot find the explanation anywhere online.

 

EDITED: I like the explanations you gave me, HollyDay. I will print them out. My DD wants written proof.

Edited October 18, 2010 by distancia

[EKS]

Unless the negative sign is inside the parentheses the negative is taken *after* squaring the 3. Thus -9. It means "the negative of 3 squared," not "negative 3 squared."

 

I've recently seen this in both Foerster's Algebra II and Lial's Intermediate Algebra. I also saw it in ALEKS Algebra I.

[angela in ohio]

Okay, now you ladies have told me this: where have you seen it actually written? My sweet sunshine DD :mad: likes to see it in writing. Hearing it from another source--even a teacher--doesn't cut it. I cannot find the explanation anywhere online.

 

EDITED: I like the explanations you gave me, HollyDay. I will print them out. My DD wants written proof.

 

I know it is in Saxon Algebra 1/2, because I taught it to a group of students last year. I don't like Saxon, bu they did cover this well. :D

[Julie of KY]

It's written in Art of Problem Solving Algebra - not that this helps you. :)

[Guest Cheryl in SoCal]

Okay, now you ladies have told me this: where have you seen it actually written? My sweet sunshine DD :mad: likes to see it in writing. Hearing it from another source--even a teacher--doesn't cut it. I cannot find the explanation anywhere online.

 

EDITED: I like the explanations you gave me, HollyDay. I will print them out. My DD wants written proof.

 

Dr Demme addresses this but I can't recall which whether it's in Pre-Algebra or Algebra 1.

[Teachin'Mine]

I did some quick searching of Khan, but couldn't find it - but I would recommend looking there. I did find this from Dr. Math:

 

http://mathforum.org/library/drmath/view/55713.html

 

but I'm not sure it's very helpful as it suggest parentheses be used to clarify what's meant. Can you borrow a Saxon text?

Edited October 18, 2010 by Teachin'Mine

[HollyDay]

It is in Saxon 1/2 and Saxon Algebra 1. Can you borrow a text?

[distancia]

Cheryl, you're right--it is in MUS Pre-Algebra, both the book and the video. My D learned this from both sources, then promptly forgot it 2 weeks later.

 

I refreshed her with the Pre-Algebra book. She asked the "why" behind it. I believe it has to do with the "multiplicative identity element of 1". I do know that as soon as I start rattling off the words my D loses all interest.

 

About the Saxon, I'll see if I can dig up a copy.

[Dana]

Here you go... in print :)

 

The demonstration I often give is that if you were going to simplify

12-3^2, your next step would be 12-9 (you certainly wouldn't write 12+9).

If the 12 weren't there, you'd have

-3^2 = -9.

 

With exponents it's really important to tell what the base is.

With -3^2, the base is 3, and you're taking the opposite of it.

With -x^2, the base is x, and you're taking the opposite of it (or multiplying by the coefficient, -1).

 

This trips up a lot of people, so it's good to spend enough time and practice now to recognize the difference. Note that some calculators will do the computation correctly and others won't, so be careful with relying on calculators as well.

[Guest Cheryl in SoCal]

Cheryl, you're right--it is in MUS Pre-Algebra, both the book and the video. My D learned this from both sources, then promptly forgot it 2 weeks later.

 

I refreshed her with the Pre-Algebra book. She asked the "why" behind it. I believe it has to do with the "multiplicative identity element of 1". I do know that as soon as I start rattling off the words my D loses all interest.

 

About the Saxon, I'll see if I can dig up a copy.

I wasn't trying to imply that she should know it because it was in MUS and I'm really sorry if I came across that way! I was answering the question about where the reason would be in print and mentioned MUS because I know you have been using it:001_smile: Is the written explanation in MUS not enough?

 

There is a math handbook series called Math on Call (well, that's one of them anyway) and there is one for algebra called Algebra to Go. It goes through all the rules, etc for Algebra. I think your daughter would find it helpful. I own it and really like it for when I need to look us something quickly vs trying to find it in MUS's TM. It has nothing but 5 star reviews on Amazon.

 

http://www.amazon.com/Algebra-Go-Mathematics-Handbook-Handbooks/dp/0669471526/ref=sr_1_5?ie=UTF8&qid=1287411783&sr=8-5

 

Algebra To Go is a unique new handbook designed to help demystify algebra for students. Modeled after the Math On Call handbook, Algebra To Go is a student-friendly resource that covers key and often complex math topics in a way that's clear and easily understandable for students - from numeration and number theory to estimation, linear and non-linear equations, geometry, and data analysis.

Edited October 18, 2010 by Cheryl in SoCal

[Kareni]

There is a math handbook series called Math on Call (well, that's one of them anyway) and there is one for algebra called Algebra to Go.

 

 

I like these books from Great Source too. (And I happen to have copies for sale here on the sale board if you are interested.)

 

Regards,

kareni