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Multiplying Rational Expressions a la Shmoop In the distant future, arguments between friends
and roommates will be solved with math.
Today, we'll see how it might be used to solve a problem between two roommates on a space
station orbiting Jupiter.
Meet Xavier and Yumi. Their dilemma is represented by the following...
four x over five y squared times twenty x-squared y over y to the fourth.
Now let's talk about what they have in common.
We all have something in common, right?
Remember, usually when we multiply fractions, we multiply across top and bottom. But when
we see a chance, we can simplify first by canceling any duplicate factors.
Looking at our problem, we can see that the 20 in the top of the second fraction and the
5 in the bottom of the first fraction are both factors of 5. We can simplify by dividing
twenty by five to get four, and divide the five on the bottom by five to get one.
Looking at the second fraction, we can cancel the top y with the y to the fourth on the
bottom... leaving y to the power of three. Now we can just multiply across the top of
the two fractions...
four x times four x-squared equals sixteen x-cubed.
And multiply across the bottom... y-squared times y-cubed...
...remember that we multiply two terms with the same base, and we can add the two exponents...in
this case, the two and 3, to get y to the fifth.
So the answer is sixteen x cubed over y to the power of five.
And on the space station orbiting Jupiter, this result means that it's Xavier's turn
to take out the plutonium.
Don't forget to shut the airlock.