# exponents of negative numbers

#### bobisaka

##### New member
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?

#### lev888

##### Full Member
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?

Why would 25*-5 be positive?

#### Jomo

##### Elite Member
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!

+*- = -
-*+ = -
+*+ = +
-*- = +

#### JeffM

##### Elite Member
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

##### Elite Member
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?
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

##### Elite Member
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

##### Elite Member
So, basically, whether a number is negative or positive has nothing to do with exponents!