# Thread: Negative powers and study habits

1. ## Negative powers and study habits

3^{-2}=9 yes? Because -3*-3 cancel out

2. oh and 2^-1/2^3 = 2^4???

3. Originally Posted by Mukilab
3^{-2}=9 yes? Because -3*-3 cancel out
$3^{-2}=\frac{1}{9}$

4. Originally Posted by Mukilab
3^{-2}=9 yes? Because -3*-3 cancel out
to supplement what Plato said, I just want to clear up your misunderstanding here. In particular, negative powers do not affect the sign of the base number

$-3 \cdot -3 = (-3)^2 = 9$

while,

$3^{-2} = \frac 1{3^2} = \frac 19$

As you can see, the sign of the base number and the sign of the power do different things. Please review the laws of exponents!

6. Note I do not know the law of exponents. I am self studying and self teaching myself for an exam. I do not know where to find resources so I just do questions.

By self teaching myself for an exam I mean that I have been given no basic background at all. No teachers or school or anything :/

7. Originally Posted by Mukilab
I will give you the rule, see what you can do with it: for a real number $x \ne 0$ and a constant $a > 0$, $x^{-a} = \frac 1{x^a}$

Originally Posted by Mukilab
Note I do not know the law of exponents. I am self studying and self teaching myself for an exam. I do not know where to find resources so I just do questions.
Well, that's a problem! doing math is largely about following rules.

If you are self studying, what are you studying from? Any math book that deals with this topic will have the rules in it. As an alternative, it is pretty easy to type "laws of exponents" into google or any search engine of your choice.

8. Furthermore

b^-2/b^3 = b^-5?

9. Originally Posted by Mukilab
Furthermore

b^-2/b^3 = b^-5?
Another rule: $\frac {x^a}{x^b} = x^{a - b}$. again, x is nonzero. so yes, you are correct

10. Originally Posted by Jhevon
I will give you the rule, see what you can do with it: for a real number $x \ne 0$ and a constant $a > 0$, $x^{-a} = \frac 1{x^a}$

Well, that's a problem! doing math is largely about following rules.

If you are self studying, what are you studying from? Any math book that deals with this topic will have the rules in it. As an alternative, it is pretty easy to type "laws of exponents" into google or any search engine of your choice.
Thank you for that rule.

I have a workbook but I have not used it yet. I am using past papers and any problems I come across I post on this forum. Since the past papers are relatively generic, they tend to have the same questions. I'm hoping the exam follows this. It seems to get easier by the year anyway. In the 2003 paper I was dealing with frustums which have incredibly annoying formulas while in 2008 it was only rectangles with cuboids in 2009.

11. Originally Posted by Mukilab
Thank you for that rule.

I have a workbook but I have not used it yet. I am using past papers and any problems I come across I post on this forum. Since the past papers are relatively generic, they tend to have the same questions. I'm hoping the exam follows this. It seems to get easier by the year anyway. In the 2003 paper I was dealing with frustums which have incredibly annoying formulas while in 2008 it was only rectangles with cuboids in 2009.
A much better way to study is to go through the workbook. if you need to, go over the topics covered on the exam from another source. the way you are studying now will not be very effective. at the very least, use the past exam as a guide for what you should be focusing on. but you need to go through the topics and learn the rules before attempting to do the problems.

12. Originally Posted by Jhevon
A much better way to study is to go through the workbook. if you need to, go over the topics covered on the exam from another source. the way you are studying now will not be very effective. at the very least, use the past exam as a guide for what you should be focusing on. but you need to go through the topics and learn the rules before attempting to do the problems.
I did my Chemistry A-Level revision with past papers so it can work for some people.

Personally, I found past papers very effective but only where there was a mark scheme nearby detailing the answers. It just goes to show that maths is about trying everything and seeing what works for you

13. Originally Posted by Jhevon
A much better way to study is to go through the workbook. if you need to, go over the topics covered on the exam from another source. the way you are studying now will not be very effective. at the very least, use the past exam as a guide for what you should be focusing on. but you need to go through the topics and learn the rules before attempting to do the problems.
Originally Posted by e^(i*pi)
I did my Chemistry A-Level revision with past papers so it can work for some people.

Personally, I found past papers very effective but only where there was a mark scheme nearby detailing the answers. It just goes to show that maths is about trying everything and seeing what works for you
Ok thanks for the feedback

14. Originally Posted by e^(i*pi)
I did my Chemistry A-Level revision with past papers so it can work for some people.

Personally, I found past papers very effective but only where there was a mark scheme nearby detailing the answers. It just goes to show that maths is about trying everything and seeing what works for you
i'm sure you didn't use ONLY the past papers. you had to consult some other resources at some point. problems don't tell you how to solve them. moreover, just asking people how to do specific problems is not a good way to study. if the exam has any surprises, which it will, you won't know how to deal with them. because you never learned a process, you never learned the method, so you would not be able to pick out what's relevant from what's not or how to tweek the solution you got from someone else in order to apply it to this new problem. furthermore, under the pressure of an exam, if you go in KNOWING that you don't know what these problems are about but only memorized a bunch of solutions, you are going to forget some of what you memorized. forgetting a solution is easy, forgetting a method is hard.

i never said don't use past papers. in fact, i recommend using past papers. i used them when i was doing O and A-levels, and i use them when i was in college. what this user is doing is not what you or i did.

15. Originally Posted by Jhevon
i'm sure you didn't use ONLY the past papers. you had to consult some other resources at some point. problems don't tell you how to solve them. moreover, just asking people how to do specific problems is not a good way to study. if the exam has any surprises, which it will, you won't know how to deal with them. because you never learned a process, you never learned the method, so you would not be able to pick out what's relevant from what's not or how to tweek the solution you got from someone else in order to apply it to this new problem. furthermore, under the pressure of an exam, if you go in KNOWING that you don't know what these problems are about but only memorized a bunch of solutions, you are going to forget some of what you memorized. forgetting a solution is easy, forgetting a method is hard.

i never said don't use past papers. in fact, i recommend using past papers. i used them when i was doing O and A-levels, and i use them when i was in college. what this user is doing is not what you or i did.

Do you recommend any maths GCSE book I should study from? I got the CGP workbook...

Page 1 of 2 12 Last