Math

5 to the negative 2 is defined as 1 divided by 5 to the 2nd power. This is 1/25.

(A^x)/(A^y) = A^(x-y)

Let (x-y)=Q

If x<y, then Q<0

So...

1/25 = 1/(5^2) = (5^0)/(5^2) = 5^(0-2) = 5^(-2)

Patiodog,

That elegant explanation depends on the questioner knowing that (anything)^0=1.
That is unlikely given that he didn't know what a negative power was !

Perhaps an easier answer to the question "why?" is to look at the "halfing rule" in the series of decreasing powers of 2

2^3 = 8
2^2 = 4
2^1 = 2
2^0 = 1
2^-1 = 1/2
2^-2 = 1/4
etc

Well, it is probably a good thing for tanya to know.

When I was in grade school, the teachers thought I might have a learning disability because I was so bad at math. Once I'd seen enough different explanations to find some that made sense to me, I did all right -- A in college calculus, near-perfect score on SAT math section and perfect score on GRE math sections.

Which isn't to brag, but just to offer an example of someone who seemed fundamentally deficient really was just waiting for something to click...

Teach me, dog. Show me the way of the number.

I don't do much with them any more.

But the trick for retarded young me was to learn numbers as geometry instead of quantities, I think.






There were a lot of drugs around the house when I was very little...