Crossing out units

[NicoJones_1B]

How does the s^-2 get crossed out of the set up of (kgm^2s^-2)(s)/(kg(m.s^-1)? Professor Lavelle went over this in class 10/11/19, but from my side of the room I could not see how every unit, but meters was crossed out.

[Akshay Chellappa 1H]

Because you are multiplying s^-2 by s in the numerator you need to add their exponents, in this case -2 and 1, which leaves you with s^-1. This is also canceled out because you are dividing by s^-1, which means you need to subtract -1 from -1, which ultimately leaves you with 0 and cancels out seconds.

[SMIYAZAKI_1B]

If you ever forget, you can always think about the exponent rules from Algebra. As long as the base number or variables are the same and they are dividing each other, (in this case, the variable is s) you can subtract the exponent of the numerator from the denominator. Since any number to 0 is 1 according to the exponent rules, you can replace the value by 1 which pretty much disappears from the equation.

[Abhi Vempati 2H]

As @Akshay Chellappa 1H mentioned, the numerator term for the equation has the units J * s. Although J is kg * m^2 * s^-2, the J will be multiplied by the s to cancel out part of the s^-2, making the numerator kg * m^2 * s^-1 (Note the s^-1 instead of the s^-2).

Then, the overall fraction will be (kg * m^2 * s-1) / (kg * m/s). This is the easy part, as the denominator terms cancel out with the numerator terms, leaving you with m as the final unit.