# Multiply. write answer is lowest form.?

• Jun 22nd 2012, 10:09 AM
Multiply. write answer is lowest form.?
Multiply. write answer is lowest form.
-11y^4 times 49y^6
_____ _______
7y^4 times 121y
it's a fraction and the line is seperating top from bottom.
i did -1.11.7.7.y^4.y^6
______________ then i did 11.7y^5 times -7y^5
7.11.11.y.y^4 ______ ______
11.7y^5 11

I don't get how i got y to the 5th powered? or what to do next
• Jun 22nd 2012, 11:25 AM
HallsofIvy
Re: Multiply. write answer is lowest form.?
So this is $\frac{-11y^4}{7y^4}\frac{49y^6}{121y}$?
I presume you immediately noticed that $49= 7^2$ and $121= 11^2$.

Quote:

i did -1.11.7.7.y^4.y^6
Okay, that is $-1.11.7.7y^10$ because $y^ay^b= y^{a+ b}$
in the numerator
and you have 7.11.11.y.y^4 which is $7.11.11.y.y^= 7.11.11.y^{4+1}= 7.11.11.y^5$
in the denominator.
$\frac{-1.11.7.7.y^{10}}{7.11.11.y^5}$ and you should see that one "11" in both numerator and denominator will cancel and that one "7" in both numerator and denominator will cancel so you have
$\frac{-1.7.y^{10}}{11.y^5}$.

Now, as always in mathematics, you can do that in several different ways. First, you can write, or imagine, that " $y^{10}$" as 10 separate "y"s in the numerator and the " $y^5$" in the denominator as 5 separate "y"s in the denominator and cancel 5 of them leaving " $y^5$" in the numerator. Or you could "move" that "$y^5$" into the numerator where it becomes " $y^{-5}$". And then, of course,
you have $y^{10}y^{-5}= y^{10+(-5)}= y^5$. Finally, you could use the exponent law derived in that way- $y^a/y^b= y^{a- b}$ so that $y^{10}/y^5= y^{10- 5}= y^5$.