How do you simplify expressions with powers when there are two division problems that you have to multiply?

Question

I can simplify expressions with powers if all you have to do is multiply, but I'm stuck on some more difficult problems. One of the problems I have to do is:

(x^2y)/(3y^3x^3) times (18x^4y^2)/(xy^6)

I'm not sure if you cross multiply or multiply regularly. Or if you have to simplify each side of the problem first?

Thanks!

Answer 1

Multiply regularly. Or you can simplify both first, then multiply...
(x^2y)/(3y^3x^3) * (18x^4y^2)/(xy^6) = 1/(3y^2x) * (18x^3)/(y^4) = (18x^3)/(3y^6x) = (6x^2)/(y^6)

Answer 2

When you multiply expressions you add the power, when you divide you subtract.

(x^2y)/3y^3x^3)= 1/(3y^2x)
(18x^4y^2)/(xy^6) = (18x^3)/y^4

1/(3y^2x) * (18x^3)/y^4 = 6x^2/(y^6)

Of course you can do them all in one step and add and subtract all the power of x and y...I am just trying to explain here.

Answer 3

(x^2)(y)/3(y^3)(x^3)[18(x^4) (y^2)/(x(y^6)] =
grouping numerator terms and denominator terms
(x^2)(y)[18(x^4)(y^2)]/[3(y^3) (x^3) (x) (y^6) =
grouping x terms and y terms
18(x^6)(y^3)/[3(y^9)(x^4)] =
simplifying
6(x^2)/y^6)