Question

A number raised to a negative exponent is negative

Answer 1

Is that always never or sometimes?

Answer 2

\(\large\color{black}{ \displaystyle a^{-b}=\frac{1}{a^b} }\)

if *a* is positive, then *a^b* is also positive (and so is *a^(-b)* positive).

Answer 3

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*.

Answer 4

So it is never always or sometimes?

Answer 5

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*

Answer 6

`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*

Answer 7

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*.

Answer 8

@Tesslover What do you think is the answer to the question?