What are the calculation steps to simplify using laws of exponents of 18a^2 b^3 / 6ab and 2w^4 * 3w and 3a^ -2b)^2 ?

Question

I know the answer is 3ab^2 but I don't get how. Because I thought you are only supposed to add the exponents 2 and 3 and it would be 3ab^5.

Additionally, the answer for the second question is 6w^5, although there is just one exponent and it is 4.

The last calculation is 9b^2/b^4. How come the b is first (numerator) and denominator is a?

Answer 1

when you divide, you subtract exponents, not add them

w also Has an implicit exponent of 1. so w times w^4 = w^5

(3a^-2)(b))^2 = (3b/a^2)^2 = 9b^2/a^4