Question

Mathematically, what is the correct way to write a speed of 100 meters per second?

Answer 1

per means "divide". So meter per second means meter/second.
Also note that a negative power in the numerator is equivalent to a positive in the denominator.
Example:
1/s = s^-1
1/(s^2) = s^-2

Based on this:
100 meters per seconds can be written as:
100 m/s , or
100 ms^-1