This is a discussion on Powers and simplifications, please help me within the A Brief History of Cprogramming.com forums, part of the Community Boards category; Can anyone explain for me how: -24x^6y^7 --------------- 18x^-3y^9 becomes -4x^9 -------- 3y^2 ? Sorry if I am using this ...

Can anyone explain for me how:

-24x^6y^7
---------------
18x^-3y^9

becomes

-4x^9
--------
3y^2 ?

Sorry if I am using this board as a place to ask about maths.......If you have any good link to some good maths questions forum, then I'd be very glad to have it.

2. Just play around with the following two properties a bit, and you'll get it:

(x^a)*(x^b)=x^(a+b)
x^(-a)=1/(x^a)

3. Expanding the exponents you get:

-24 * x * x * x * x * x * x * y * y * y * y * y * y * y
----------------------------------------------------------------------
18 * 1/x * 1/x * 1/x * y * y * y * y * y * y * y * y * y

I bet you know that y/y = 1, so we can cross out 7 y on the top and bottom. Next, when you have a fraction on the bottom part, you can flip the bottom part of that fraction to the top of the main one. So:

a
---
b/c

...becomes ac / b.

Doing that, those 3 reciprocals of x in the bottom get on top, making 7 x on top.

Next you simplify the numbers which is real simple here. Both have a common factor of 6, so you factor that out (-24 / 6 = -4, 18 / 6 = 3).

And you end up with:

-4 * x^9
------------
3 * y^2