I am having a hard time grasping what makes something a monomial and then subsequently a polynomial. I get that division by a variable is not allowed and therefore not a monomial but why is that? I just like to make sense of these things as I find it much easier to retain if I understand something.

Also, why is something like 3^1/2x not a monomial when a square root of a constant by itself is? How is that any different than any other constant times a variable?

Thanks for the help.