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Math Help - Two exponent problems.

  1. #1
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    Jan 2009
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    Two exponent problems.

    Ok, here are two more problems involving exponents. I'm not the best mathematician, so my answers may or may not be correct. If they are incorrect, could you please show how one can reach the correct solution?

    Thank you.

    Here is the first problem:

    "simplify:"
     <br />
(7x^6y^3)(-8x^2y^6)<br />

    And my solution to same:

    -56x^8y^9


    Note that in this second problem, the "|" represents a bracket that is around the whole problem, NOT the contained numbers' absolute value:

    "simplify: "
    |-5a^3 b^4 c^0|^-4
    |3a^4 b^6 c^3 |

    and here are my steps to reaching a solution:

    -5a^-12 b^-16 1^-4
    3a^-16 b^-24 c^-12

    -5 b^-16 1^-4
    3a^-4 b^-24 c^-12

    -5
    3a^-4 b^-40 c^-12
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, blastedcody!

    Simplify: .  (7x^6y^3)(-8x^2y^6)<br />

    And my solution: . -56x^8y^9 . . . . Good!

    Simplify: . \left[\frac{\text{-}5a^3 b^4 c^0}{3a^4 b^6 c^3}\right]^{-4}

    and here are my steps to reaching a solution: .  \frac{\text{-}5a^{-12}b^{-16}1^{-4}} {3a^{-16} b^{-24} c^{-12}}
    You forgot about the coefficients . . .

    I'd reduce "inside" first: . \left[\frac{\text{-}5}{3ab^2c^3}\right]^{-4} \;=\;\frac{(\text{-}5)^{-4}}{(3)^{-4}(a)^{-4}(b^2)^{-4}(c^3)^{-4}}

    . . = \;\frac{3^4}{(\text{-}5)^4a^{-4}b^{-8}c^{-12}} \;=\;\frac{81a^4b^8c^{12}}{625}

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  3. #3
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    Thank you, that was very helpful.
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  4. #4
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    Nov 2008
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    Cool

    Your first answer is ver correct but please make the second question clearer.
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