Question 65145
To reduce to lowest form:
40x^3yz^2
--------- 
30xy^2z^4 

When dividing, you subtract exponents. When multiplying you add exponents.
Now lets rewrite the fraction:

(40)(x)(x)(x)(y)(z)(z))
-----------------------
(30)(x)(y)(y)(z)(z)(z)(z)

Now, we can start cancelling terms and see what we have left:
4x^2
-----
3yz^2

Another way to look at it is as follows:

4x^(3-1)
-------                  =
3y^(2-1)z^(4-2)

4x^2
----
3yz^2

We can even look at it another way:

4x^(3-1)y^(1-2)z^(2-4)
---------------------          =
        3

4x^2y^(-1)z^(-2)
---------------             
      3

but we know that y^(-1)=1/y  and z^(-2)=1/(z^2)

sooooooo we end up with the same reduced fraction as above.


Hope this helps. Happy holidays.----ptaylor