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Math Help - Multiplying/dividing with exponents

  1. #1
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    Multiplying/dividing with exponents

    I am having difficulties figuring out what exactly the author of my Algebra book is doing in regards to step 2.

    Expression
    (\frac{x^3}{y^2}^5) (\frac{x}{y})^{-2}

    Step 1= \frac{x^{15}}{y^{10}} * \frac{y^2}{x^2}

    Step 2= x^{15-2} y^{2-10}

    Could some one please clearly explain whats going on from step 1 to step 2. When the expression turns into x^{15-2} y^{2-10} is where im the most confused, if someone would please explain this transition that would be greatly appreciated. Unless the author is using \frac{a^m}{a^n}=a^{n*m} to combine BOTH fractions.

    Thanks!
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  2. #2
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    Quote Originally Posted by allyourbass2212 View Post
    I am having difficulties figuring out what exactly the author of my Algebra book is doing in regards to step 2.

    Expression
    (\frac{x^3}{y^2}^5) (\frac{x}{y})^{-2}

    Step 1= \frac{x^{15}}{y^{10}} * \frac{y^2}{x^2}

    Step 2= x^{15-2} y^{2-10}

    Could some one please clearly explain whats going on from step 1 to step 2. When the expression turns into x^{15-2} y^{2-10} is where im the most confused, if someone would please explain this transition that would be greatly appreciated. Unless the author is using \frac{a^m}{a^n}=a^{n*m} to combine BOTH fractions.

    Thanks!
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    press the green button every time.
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  3. #3
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    Yes I understand when its a single fraction using \frac{a^m}{a^n}=a^{m-n}. I am familiar with the exponent laws and in fact I have them laying out in front of me. I am just uncertain whats going on in this particular situation.
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  4. #4
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    I am no math expert, but I think this might help clarify.

    Instead of seeing it like this
    \frac{x^{15}}{y^{10}} * \frac{y^2}{x^2}

    View it as this
    \frac{x^{15}y^2}{y^{10}x^2}

    Then just use the exponent property
    \frac{a^m}{a^n}=a^{m-n} to solve the rest.

    e.g.

    15-2, 2-10 resulting in x^{13}y^{-8}
    or \frac{x^{13}}{y^8} if you want to remove negative exponents using the property a^{-n}=\frac{1}{a^n}

    But again im no expert at math, I would have someone else verify this statement. I would hate to be the source of any confusion.
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  5. #5
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    Quote Originally Posted by allyourbass2212 View Post
    Yes I understand when its a single fraction using \frac{a^m}{a^n}=a^{m-n}. I am familiar with the exponent laws and in fact I have them laying out in front of me. I am just uncertain whats going on in this particular situation.
     <br />
\frac{x^{15}}{y^{10}} \;\times\;\frac{y^2}{x^2}

     <br />
\frac{x^{15}}{x^2}\;\times\;\frac{y^2}{y^{10}}<br />

     <br />
x^{15-2}\;\times \;y^{2-10}<br />

     <br />
x^{13}\;\times \;y^{-8}<br />

     <br />
x^{13}\;\times \;\frac{1}{y^{8}}<br />

     <br />
\frac{x^{13}}{y^{8}}<br />
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  6. #6
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    Thanks both of you.

    I think the way cmf0106 set it up is easier to understand though... can anyone confirm he did it correctly?

    Thanks again guys.
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  7. #7
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    Quote Originally Posted by allyourbass2212 View Post
    Thanks both of you.

    I think the way cmf0106 set it up is easier to understand though... can anyone confirm he did it correctly?

    Thanks again guys.
    yes, he did correctly.
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