SOLUTION: 40x^3yz^2 --------- 30xy^2z^4 Write the fraction in lowest terms. I know how to reduce the numbers, but I don't know how to reduce the variables. Could someone please hel

Question 65145: 40x^3yz^2
---------
30xy^2z^4
Write the fraction in lowest terms.

I know how to reduce the numbers, but I don't know how to reduce the variables. Could someone please help me out? Thank you.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
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

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