Index Laws?

Question

I have a terrible dilemma, im stuck with how to work out the denominator on an index equation.

its 3x^6y^4
-----------
12xy^3

how do i work out what number goes on the bottom? i know the number is four, but how do i get that number? plz help. I have a maths test tomorrow

Answer 1

Deal with constants, x terms and y terms separately.

Constants: 3/12 = 1/4
x: x^6/x = x^(6-1) = x^5
y: y^4 / y^3 = y^(4-3) = y^1 = y

So the answer is x^5y / 4.

Answer 2

( 3x^6 y^4 ) / (12x y^3)
You have x^6 on top and x (which is x^1) on the bottom.
Subtract index 1 from index 6 to get index 5 on the top, and then you will have no x on the bottom.
That gives (3x^5 y^4) / (12y^3).
Do the same thing (4 - 3 = 1) with the y indices.
That gives (3x^5y)/12
Again, you have no y left on the bottom.
Now note that the 3 on top divides into the 12 on the bottom 4 times.
You can therefore replace the 12 with 4, and get rid of the 3.
That gives x^5y/4, which is the answer.
It does not matter that you have no x or y on the bottom.