exponents of negative numbers

bobisaka

New member
Joined
Dec 25, 2019
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28
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?
 

lev888

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Jan 16, 2018
Messages
913
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?
Why would 25*-5 be positive?
What about negative exponents?
 

Jomo

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Dec 30, 2014
Messages
5,407
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!
 

Jomo

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Dec 30, 2014
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5,407
+*- = -
-*+ = -
+*+ = +
-*- = +
 

JeffM

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Sep 14, 2012
Messages
4,334
It is unclear what you are asking.

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

\(\displaystyle a,\ b \in \mathbb R, \ a > 0, \text { and } b > 0 \implies a^{-b} = \dfrac{1}{a^b} = \left ( \dfrac{1}{b} \right )^b \in \mathbb R.\)

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.

\(\displaystyle a \in \mathbb R,\ a < 0, \text { and } b \in \mathbb Z \implies\)

\(\displaystyle a^{(2b)} = (-\ a)^{2b} \in \mathbb R \text { and } a^{(2b-1)} = -\ (-\ a)^{(2b-1)} \in \mathbb R.\)
 

pka

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Jan 29, 2005
Messages
9,279
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?
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.
 

JeffM

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Sep 14, 2012
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4,334
There was a typo in my previous post.

\(\displaystyle a,\ b \in \mathbb R, \ a > 0, \text { and } b > 0 \implies a^{-b} = \dfrac{1}{a^b} = \left ( \dfrac{1}{a} \right )^b \in \mathbb R.\)
 

HallsofIvy

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Jan 27, 2012
Messages
5,641
So, basically, whether a number is negative or positive has nothing to do with exponents!
 
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