A number raised to a negative exponent is negative

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A number raised to a negative exponent is negative

Mathematics
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Is that always never or sometimes?
\(\large\color{black}{ \displaystyle a^{-b}=\frac{1}{a^b} }\) if *a* is positive, then *a^b* is also positive (and so is *a^(-b)* positive).
Only when *b* is odd, and *a* is negative, (like (-5)^3) will you get a negative result, and if a^b is negative then *a^(-b) = 1/a^b =negative*.

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So it is never always or sometimes?
So there are times when *a^(-b)* is negative, but certainly not always: Some examples of different results: *2^(-2) = 1/2^2 = 1/4* *(-4)^(-2) = 1/(-4)^2 = 1/16* *(-1)^(-1) = 1/(-1)^1 = 1/(-1)=-1* *(-2)^(-3) = 1/(-2)^3 = 1/(-8)=-1/8*
`A positive number is raised to a negative exponent:` *is always positive* `A negative number is raised to negative exponent:` *is positive when exponent is even* AND *is negative when exponent is odd*
And if you say just *a number*, then that could be *either positive or negative* and thus the result can be *either positive or negative*.
@Tesslover What do you think is the answer to the question? |dw:1444265489958:dw|

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