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Math Help - Multiply. write answer is lowest form.?

  1. #1
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    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
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  2. #2
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    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.

    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 "[itex]y^5[/itex]" 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.
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