exponents of negative numbers

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bobisaka

Junior Member
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Dec 25, 2019
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Do they go from negative to positive, positive to negative?
-5*-5=25, than 25*-5 = -125

OR

would the exponents continue being positive after each conscecutive multiplication?

and what about negative exponents?
 
bobisaka said:
Do they go from negative to positive, positive to negative?
-5*-5=25, than 25*-5 = -125

OR

would the exponents continue being positive after each conscecutive multiplication?

and what about negative exponents?
Click to expand...
Why would 25*-5 be positive?
What about negative exponents?
 
By definition x-1 is 1/x

So for example x-5= (x-1)5 = (1/x)5 = 1/x5.

In general x-n= 1/xn.

In your post you have no exponents!
 
It is unclear what you are asking.

If you are asking about raising a positive number to negative power, things are simple.

[MATH]a,\ b \in \mathbb R, \ a > 0, \text { and } b > 0 \implies a^{-b} = \dfrac{1}{a^b} = \left ( \dfrac{1}{b} \right )^b \in \mathbb R.[/MATH]
If you are asking about raising negative numbers to a power, that is not a problem if you are talking about integer powers, but rational powers take you outside the real number system.

[MATH]a \in \mathbb R,\ a < 0, \text { and } b \in \mathbb Z \implies[/MATH]
[MATH]a^{(2b)} = (-\ a)^{2b} \in \mathbb R \text { and } a^{(2b-1)} = -\ (-\ a)^{(2b-1)} \in \mathbb R.[/MATH]
 
bobisaka said:
Do they go from negative to positive, positive to negative?
-5*-5=25, than 25*-5 = -125 OR would the exponents continue being positive after each consecutive multiplication?
and what about negative exponents?
Click to expand...
To bobisaka, here is my suggestion to you: learn basic middle school (5th, 6th, 7th) grade mathematics before you confuse yourself beyond all possible recovery. Not doing so can mean that you remain mathematically illiterate for life. Please go back to the basics.
 
There was a typo in my previous post.

[MATH]a,\ b \in \mathbb R, \ a > 0, \text { and } b > 0 \implies a^{-b} = \dfrac{1}{a^b} = \left ( \dfrac{1}{a} \right )^b \in \mathbb R.[/MATH]
 
So, basically, whether a number is negative or positive has nothing to do with exponents!
 
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