Question 161452This question is from textbook Beginning Algebra
: Hi, I'm having a real difficult time understanding why the answer to the following problem is like it is.
x^3y^2/5xy6
My text book shows the answer as x^2/5y^4
Why does x go in the numerator, and y in the denominator?
My text book fails to explain why this is.
When subtracting the y exponents, the larger number is the denominator, and the smaller number is in the numerator, so shouldn't the end result look like this:
1/5x^2y^4
I can't get past this. I'd really appreciate any help.
This question is from textbook Beginning Algebra
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! When you see:
x^3/x^2
You could rewrite it as:
(x*x*x)/(x*x)
Now, for each matching pair of x (one in the numerator and one in the denominator) you can "cancel" it out. Since, there are two pairs, you can cancel out two x's in the numerator and two x's in the denominator leaving:
x/1
or
x
.
.
Similarly, for your:
x^3y^2/5xy^6
Looking at just the x's:
(x*x*x)y^2/5xy^6
Notice, there is only ONE pair of x's so canceling them out gives:
(x*x)y^2/5y^6
or
x^2y^2/5y^6
.
Looking at just the y's:
x^2(y*y)/5(y*y*y*y*y*y)
Since there are two pairs of y's, we can cancel two from the numerator and two from the denominator:
x^2/5(y*y*y*y)
or
x^2/(5y^4)
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