# Negative exponents and calculation rules

1. Feb 21, 2006

### runicle

I just want to know if a negative exponent is as just the same as saying one over another number.
For example:
5^1/3 = 5^-3

Another thought
would base numbers only affect base numbers and exponents only affect exponents?

Last edited: Feb 21, 2006
2. Feb 21, 2006

### assyrian_77

No, that is not right. To put it in your word: a negative exponent is the same as saying one over the whole number. In other words:

$$x^{-a}=\frac{1}{x^a}$$

3. Feb 21, 2006

### runicle

oops i meant to say

4. Feb 21, 2006

### assyrian_77

.

Anyway, it it still not correct. See my previous post.

5. Feb 22, 2006

### HallsofIvy

Staff Emeritus
That would be saying $a^{-x}= \frac{a^1}{something}$, wouldn't it?? That, of course, is wrong. Again
$$a^{-x}= \frac{1}{a^x}$$

6. Feb 22, 2006

### arildno

Eeh? Come again?
This is just incomprehensible.

7. Feb 22, 2006

### runicle

Just figured it out in the calculator,

8. Feb 23, 2006

### HallsofIvy

Staff Emeritus
Figured out what? Are you saying you now know how to simplify something like $\frac{a^6}{a^{-4}}$ or are you just saying you'll let your calculator do it for you?

9. Feb 23, 2006

### runicle

No i just put 2^2 gave me an answer 2^1/2 gave me an answer 2^-2 gave me an answer and none of the answers were the same.

10. Feb 24, 2006

### topsquark

Specifically, $$5^{1/3}=\sqrt[3]{5}$$ and $$5^{-3}=\frac{1}{5^3}$$

Not sure what you mean by your second question. Do you have an example in mind?

-Dan

11. Mar 1, 2006

### runicle

It's not a question i just wanted to know the question previous to that dilemna had any way to relate to the dilemna. For even lamens terms:
1st part of first question.
2 over 3 is exactly the same as 4 over 6 only its simplified.
would 5^-3 be the same as 5^1/3? (Yes it does)
In number 2*2 = 4, 2^2*2^2 = 2^4, you know what i mean... example of a problem.
3(2x*3) = 6x*9 notice 3 outside of the brackets affect the numbers inside of it? If the 2x was 2x^2 would it be then after 6x^6*9.

Sorry, my english. I am trying to improve on it, please correct my grammar if you can. (It was all a misunderstanding, lol)

12. Mar 1, 2006

### chroot

Staff Emeritus
No. 5^-3 = 0.008.

5^(1/3) = 1.70998

The reason they're different is because the exponents are different. If -3 does not equal 1/3 (it does not) then 5^-3 cannot equal 5^(1/3).

- Warren

13. Mar 1, 2006

### d_leet

No

3(2x*3) = 6x*3 you essentiall multiplied by 9. and lets say you have just x2 for a second if you multiply that by 3 you get 3x2 not 3x6 The exponent is unaffected because you don't know for sure if x = 3 or what x equals

14. Mar 2, 2006

### VietDao29

No, you should know that:
$$\sqrt[n] {a ^ m} = a ^ {\frac{m}{n}}$$.
And:
$$a ^ {-m} = \frac{1}{a ^ m}$$.
This is due to:
$$\frac{a ^ m}{a ^ n} = a ^ {m - n}$$.
So:
$$a ^ {-m} = a ^ {0 - m} = \frac{a ^ 0}{a ^ m} = \frac{1}{a ^ m}$$
Since a0 = 1 for all a <> 0.
$$5 ^ {\frac{1}{3}} = \sqrt[3] {5} \approx 1.71$$, whereas:
$$5 ^ {-3} = \frac{1}{5 ^ 3} = \frac{1}{125} = 0.008$$.
And of course you know that:
0.008 <> 1.71, right? :)

15. Mar 2, 2006

### runicle

correct me if i'm wrong
Question=(2x+2)(3x+3)
-Foiled
=6x^2+6x+6x+6
=6x^2+12x+6
so....
3(2x+3) = 6x+9 (so side note to that) 3(2x*3)= 6x*3
so....
2^1/3 = 3v--2 and 2^-3 = 1/2^3 = 1/8
so....
can anyone give me some good ways of remembering this stuff? Or atleast tips?

16. Mar 2, 2006

### chroot

Staff Emeritus
Everything you've posted looks correct, runicle. I'd advise that you use the notation sqrt(2) instead of "v--2" to represent the square root, or use the latex features built into the site.

How to remember this stuff? Most of it becomes second nature once you being using it a bit. Which of your "operations" are you having trouble remembering?

- Warren

17. Mar 2, 2006

### moose

Do 30 problems and I would think that you would know every single thing without thinking about it anymore.

18. Mar 3, 2006

### runicle

I am still a little fuzzy with what happens when you add, multiply exponents and what and what not can you add or multiply with. Like as an example 2x^2 + 2x can't be added... Do you catch my drift? Along with what you can and cannot do when doing certain tasks. Is there a very good website that can tell you right away what expressions or equations would bring you to know common tasks?

19. Mar 4, 2006

### VietDao29

My suggestion is that you should go over your textbook again thoroughly, try to understand the concept, then try your hands on some problems, and remember the formulae.
$$a ^ x \times a ^ y = a ^ {x + y}$$
$$\frac{a ^ x}{a ^ y} = a ^ {x - y}$$
---------------
Now of course, you cannot "add" 2x2 + 2x to get 4x2 or 4x. Just think like this:
Writing 3x2 means that you have three x2's (it's like you have 3 apples), 5x2 means that you have five x2's. If you add them together, you'll have 8 x2's, right?
3x2 + 5x2 = 8x2.
Now 3x2 + 2x cannot be added since x is not the same as x2, you cannot add 3 apples, and 2 orranges, right? However, it can be factored like this:
3x2 + 2x = x(3x + 2).
Can you get this? :)

20. Mar 4, 2006

### HallsofIvy

Staff Emeritus
Yes, that's correct.
I wish you wouldn't use different symbols for the same thing!
Does (2x*3) mean the same as 2x^3? If so then both of those are correct.
It took me a while to figure that out! the v-- thing is a root!
Yes, $2^{\frac{1}{3}}= ^3\sqrt{2}$. Click on that to see the LaTex code I used.

Yes, that also is true.
The same way you get to Carnegie Hall- practice, practice, practice! Do lots of homework problems. If you teach assigns half the exercises on a page- do all of them!