Question

{27a^4b^3} {66x^6y^6}
________ *_________
{22x^3y^3} {36a^6b^3}

Answer 1

notice you have no addition or subtraction, so canceling will work very well.
On the side in rough do
27(66)/(22(36))
= 1/4 , after dividing top and bottom by 9, by 11, by 2 and by 4

the a's : a^4/a^6 = 1/a^2 , so a^2 at the bottom
the b's : b^3/b^3 = 1 , so they will just cancel
the x's : x^6/x^3 = x^3 , goes to the top
the y's : y^6/y^3 = y^3 , goes to the top

so our answer is

(1/4)x^3 y^3 /a^2
or
x^3y^3/(4a^2)