## anonymous one year ago A number raised to a negative exponent is negative

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1. anonymous

Is that always never or sometimes?

2. SolomonZelman

$$\large\color{black}{ \displaystyle a^{-b}=\frac{1}{a^b} }$$ if *a* is positive, then *a^b* is also positive (and so is *a^(-b)* positive).

3. SolomonZelman

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*.

4. anonymous

So it is never always or sometimes?

5. SolomonZelman

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*

6. SolomonZelman

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*

7. SolomonZelman

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*.

8. Directrix

@Tesslover What do you think is the answer to the question? |dw:1444265489958:dw|