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Math Help - Simplify/solve/factor

  1. #1
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    Simplify/solve/factor

    How do I solve/simplify this:
    ((2a^-2 b^4) / (4a^3 b^-2))^-2
    Do I do the ^-2 to everything inside first? Or what steps do I do first?

    And how do I factor this:
    x^2-7x+12

    I don't remember completely as I haven't done it in years, but it has to add up to -7 and multiply together to 12? Or something along those lines...

    Any help would be great, thanks.
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  2. #2
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    hi there, please consider the following step to get you started.

     \left(\frac{2a^{-2} b^4}{4a^3 b^{-2}}\right)^{-2} = \left(\frac{4a^3 b^{-2}}{2a^{-2} b^4}\right)^{2}

    Now square every term inside the bracket then simplify.
    Last edited by pickslides; November 9th 2009 at 03:57 PM. Reason: Bad Latex
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  3. #3
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    Quote Originally Posted by alfer22 View Post
    H

    And how do I factor this:
    x^2-7x+12

    I don't remember completely as I haven't done it in years, but it has to add up to -7 and multiply together to 12? Or something along those lines...

    yes, a and b are factors of 12 that give you a+b = -7

    factored form will be (x+a)(a+b)

    Spoiler:
     x^2-7x+12 = (x-3)(x-4)
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  4. #4
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    Quote Originally Posted by pickslides View Post
    hi there, please consider the following step to get you started.

     \left(\frac{2a^(-2) b^4}{4a^3 b^{-2}}\right)^{-2} = \left(\frac{4a^3 b^{-2}}{2a^{-2} b^4}\right)^{2}

    Now square every term inside the bracket then simplify.
    So whenever something is bracketed by a negative exponent you flip the inside and change the exponent to positive?
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  5. #5
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    correct.
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  6. #6
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    \left(\frac{8y^6 z^{\left(\frac{2}{3}\right)}}{x\left(\frac{1}{3}\r  ight)}\right)^{3}

    I am clueless on how to deal with the fraction exponents.

    The final answer should come to 512xy^{18}z^{2}, but I do not know how to get there.

    Any help would be great.
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  7. #7
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    I think you mean?

     \left(\frac{8y^6 z^{\frac{2}{3}}}{x^\frac{1}{3}}\right)^{3}<br />

    If so multiply the 3 into each term

     \frac{8^3y^{6\times 3} z^{\frac{2}{3}\times 3}}{x^{\frac{1}{3}\times 3}}

     \frac{512y^{18} z^{2}}{x^{1}}

     512x^{-1}y^{18} z^{2}
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  8. #8
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    If I have something like:
    (x^{3}y^{-\left(\frac{1}{2}\right)})^{-2}

    How do I deal with the negative exponent then?
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  9. #9
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    Remember these rules

     a^{-n} = \frac{1}{a^n}

    and

     \frac{1}{a^{-n}}=a^{n}
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