- Thread starter bobisaka
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Why would 25*-5 be positive?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?

What about negative exponents?

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.

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

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

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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.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?

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