integer squared by negative

[starssin10]

Hi, I saw an recording by Emily introducing Quantitative Comparisons of GRE.

She said when 10 is squared by negative integer the result is always positive integer.

For example, 10^-2 =positive integer.

But I am not sure how it can work, and I wonder it just validate on 10 or all positive integer.

I tried with 3 and all the results were positive. 3^-2, 3^-6....

Could you please explain how it does work or about the principle? Thanks.

[kareemmasud]

raising a number to to a negative index only means the inverse of that number, e.g. if you say 4^-2, it simply means 1/4^2. In cases like this the resulting answer will always be positive. But in cases of -4^-3, what will the result be? It is just -(1/4) * -(1/4) * -(1/4). This will be negative because the index is odd, if the index is even say 4 then it will be positive, try it yourself doing -8^-4

[tommywallach]

Exactly right!

And be careful, you said that it would always be a positive INTEGER result (when raising an integer to a negative), but you meant it will always be a positive NUMBER. It's rarely an integer (i.e. 10^-2 = 1/100).

-t