what property does this physics formula find?

Bulk coefficient of expansion, also known as volume expansivity.

It's the fractional change in volume per kelvin (or per degree, if you prefer). Since fractional change has no units - it's just a fraction - the quantity has units simply "per kelvin" or "per degree".

This is written as K to the power -1 (K^-1) , or similarly for degrees.

Algebraic arithmetic is used in anything that pertains to mathematics. Like a square's not a rectangle but a rectangle is a square, algebra's not trig but trig is algebra, trig isn't calculus but calculus is trig and algebra. Physics uses all of the above. If there's a chair and someone brings up another chair, knowing there's now two chairs isn't "dependent on addition", addition is just one of the fundamental mechanisms in expressing logic. I think you're looking at algebraic arithmetic as a specific technique, as opposed to looking at it as everything.

Coefficient of thermal volume expansion.

Unit is [volume] / ([volume] x [Kelvin]) = 1/K.