Hello,

How you explain (48z^4y^-3)/(12zy^2) = (4z^3)/y^2 ?

Thank you

Let's take this one in pieces.

The 48 and 12 reduce to become a 4 on top.
The z^4 on top and z on bottom reduce to become z^3 on top.
The y^-3 on top and y^2 on bottom reduce to become y^5 on bottom.

This leaves us with (4z^3)/y^5

Is there a particular step in this process that's giving you particular trouble?

Veritas Help

Not a problem for 48 and 12 but:

1. The rules for know how to reduce: z^4 in z^3 with z?
2. Particulary how y^-3 become y^5 with y^2?
3. How to know which on stay on the top and the bottom?

Thank you

Go back and look at Math Essentials, page 99, and you will see the big table of Exponent rules --

1. z^4 over z (which is really z^1) is z^(4-1) which is z^3.
2. y^(-3) over y^3 is y^(-3-2) which is y^(-5). y^(-5) on top is the same as y^5 on bottom.
3. Generally, pieces stay where they are, unless we have a negative exponent, in which case, we switch from top to bottom. If we are reducing / canceling, the one with the bigger exponent is the one that stays and the one with the smaller exponent is the one that gets canceled.

Veritas Help