On Wed, 11 Sep 2019 13:06:10 -0700, David Paste wrote:
When writing, for example, "metres per second per second" for
acceleration, it is noted as ms^-2 (where the caret symbolises the -2 is
in superscript).

I understand that, and why, "per second per second" is "seconds
squared", but in the notation, why is it superscript minus 2? Why not
just superscript 2?

It's because it's /per/ second, indicating dividing. ms^2 would be metre-
second-seconds (i.e. distance times time times time), while acceleration
is ms^-2, metres per second per second, distance divided by time divided
by time.
Positive powers are multiplication, negative powers are division (or
"anti-multiplication"). x^2 is x*x, x^-2 is (1/x)/x. 2^2 is 4, 2^-2 is
0.25.

If you multiply acceleration (ms^-2) by time (s, or s^1), you add the
powers - and get speed in ms^(-2+1) or ms^-1. If you divide acceleration
by time, you subtract the powers - and get jerk in ms^(-2-1) or ms^-3.
The same applies starting with distance, in m, or ms^0. Anything to the
power zero is 1, so m and ms^0 are the same thing. Divide by time and you
get ms^(0-1), ms^-1.

Mike