# Negative exponents and calculation rules

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:

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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:

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

a negative exponent is as just the same as saying one over another number
oops i meant to say

a negative exponent is as just the same as saying a base number to the power of one over a number

runicle said:
a negative exponent is as just the same as saying a base number to the power of one over a number
.

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

HallsofIvy
Homework Helper
runicle said:
a negative exponent is as just the same as saying a base number to the power of one over a number
That would be saying $a^{-x}= \frac{a^1}{something}$, wouldn't it?? That, of course, is wrong. Again
$$a^{-x}= \frac{1}{a^x}$$

arildno
Homework Helper
Gold Member
Dearly Missed
runicle said:
Another thought
would base numbers only affect base numbers and exponents only affect exponents?
Eeh? Come again?
This is just incomprehensible.

Just figured it out in the calculator,

HallsofIvy
Homework Helper
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?

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.

runicle said:
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?
Specifically, $$5^{1/3}=\sqrt{5}$$ and $$5^{-3}=\frac{1}{5^3}$$

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

-Dan

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

chroot
Staff Emeritus
Gold Member
runicle said:
would 5^-3 be the same as 5^1/3? (Yes it does)
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

runicle said:
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.
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

VietDao29
Homework Helper
runicle said:
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)
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.
$$5 ^ {\frac{1}{3}} = \sqrt {5} \approx 1.71$$, whereas:
$$5 ^ {-3} = \frac{1}{5 ^ 3} = \frac{1}{125} = 0.008$$.
And of course you know that:
0.008 <> 1.71, right? :)

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?

chroot
Staff Emeritus
Gold Member
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

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

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?

VietDao29
Homework Helper
runicle said:
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?
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? :)

HallsofIvy
Homework Helper
runicle said:
correct me if i'm wrong
Question=(2x+2)(3x+3)
-Foiled
=6x^2+6x+6x+6
=6x^2+12x+6
Yes, that's correct.
so....
3(2x+3) = 6x+9 (so side note to that) 3(2x*3)= 6x*3
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.
so....
2^1/3 = 3v--2
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.

and 2^-3 = 1/2^3 = 1/8
Yes, that also is true.
so....
can anyone give me some good ways of remembering this stuff? Or atleast tips?
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!

I Barely have time to practice because i have kickboxing english homework law homework accounting homework and Math. So... If you tell me to forget about sleeping than I have no life... I wish there was a site That has everything about this kind of stuff organized, well presented and easy to remember. That would help everyone who has practically any time and just need a quick look at doing things like a minute an hour.