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Math Help - Algebra Math B level

  1. #1
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    Algebra Math B level

    Hi, i would like to recieve some help with this math problem. I have been working on it for a while but seem to be getting nowhere due to the powered negative one after the powered 3n in the first part of the fraction.
    Hopefully someone can help me and explain the steps taken.
    Thank you!

    ((x^(3n-1))^n*x^n)/((x^n)^(3n))
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Mouseman View Post
    Hi, i would like to recieve some help with this math problem. I have been working on it for a while but seem to be getting nowhere due to the powered negative one after the powered 3n in the first part of the fraction.
    Hopefully someone can help me and explain the steps taken.
    Thank you!

    ((x^(3n-1))^n*x^n)/((x^n)^(3n))
    With out LaTex I am not sure if which of these you mean

    \frac{(x^{(3n-1)^n})\cdot x^n}{(x^n)^{3n}}

    OR

    \frac{(x^{(3n-1)})^n\cdot x^n}{(x^n)^{3n}}

    and are you trying to simplify?
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  3. #3
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by Mouseman View Post
    Hi, i would like to recieve some help with this math problem. I have been working on it for a while but seem to be getting nowhere due to the powered negative one after the powered 3n in the first part of the fraction.
    Hopefully someone can help me and explain the steps taken.
    Thank you!

    ((x^(3n-1))^n*x^n)/((x^n)^(3n))
    (x^{3n-1})^{n} \times \frac{x^n}{(x^n)^{3n}}

    (\frac{x^{3n}}{x})^{n} \times \frac{x^n}{(x^n)^{3n}}

    \frac{{\color{red}(x^{3n})^{n}}}{{\color{blue}x^n}  }\times \frac{{\color{blue}x^n}}{{\color{red}(x^n)^{3n}}}=  1

    the same color same value
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  4. #4
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    Quote Originally Posted by TheEmptySet View Post
    With out LaTex I am not sure if which of these you mean

    \frac{(x^{(3n-1)^n})\cdot x^n}{(x^n)^{3n}}

    OR

    \frac{(x^{(3n-1)})^n\cdot x^n}{(x^n)^{3n}}

    and are you trying to simplify?
    It would be the second one and yes I'm trying to simplify.
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  5. #5
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    <br />
\frac{(x^{(3n-1)})^n\cdot x^n}{(x^n)^{3n}}<br />

    = <br />
\frac{x^{(3n-1)(n)}\cdot x^n}{x^{(n)(3n)}}<br />

    = <br />
\frac{x^{(3n^2-n)+(n)}}{x^{3n^2}}<br />

    = <br />
\frac{x^{3n^2}}{x^{3n^2}}<br />

    = 1

    Using the power law of exponents, (x^n)^m=x^{nm} and the multiplication law of exponents, x^{n} \cdot x^{m}=x^{n+m}, I believe this is how it is simpified, someone correct me if I am wrong; Does this help?
    Last edited by Kasper; June 11th 2009 at 11:01 AM.
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  6. #6
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by Kasper View Post
    <br />
\frac{(x^{(3n-1)})^n\cdot x^n}{(x^n)^{3n}}<br />

    = <br />
\frac{x^{(3n-1)(n)}\cdot x^n}{x^{(n)(3n)}}<br />

    = <br />
\frac{{\color{red}x^{(3n^2-n)(n)}}}{x^{3n^2}}<br />

    = <br />
\frac{x^{3n^3-n^2}}{x^{3n^2}}<br />


    Using the power law of exponents, (x^n)^m=x^{nm}, I believe this is how it is simpified, someone correct me if I am wrong; Does this help?
    the red is wrong the correct should be like this

    = <br />
\frac{x^{(3n-1)(n)}\cdot x^n}{x^{(n)(3n)}}<br />

    \frac{{\color{blue}x^{(3n^2-n)+n} }}{x^{(n)(3n)}} the blue should be instead of the red

    because in multiple the powers add not multiply right
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  7. #7
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    Yeah I'd already corrected that after you started replying, haha. Sorry for the confusion, edited it 7 minutes before you posted, heh. Love forum timers.
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