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View Full Version : Powers and simplifications, please help me



Zewu
12-21-2003, 06:52 PM
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.

Zach L.
12-21-2003, 07:04 PM
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)

Speedy5
12-21-2003, 07:09 PM
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