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Math Help - Multiplying different bases with different exponent

  1. #1
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    Multiplying different bases with different exponent

    I'm doing a very basic pre algebra "refreshment", and for an assignment I need to simplify the following, leaving my answer as a single base raised to a single exponent:

    9^2 * 12^3 * 2

    I can't seem to find the steps needed to get the answer which is supposed to be 6^7. Normally I would look for common bases (like 9 and 27 have 3 in common), but I don't see that in 9 and 12.

    Can someone explain this to me?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Re: Multiplying different bases with different exponent

    Quote Originally Posted by timmeh View Post
    I'm doing a very basic pre algebra "refreshment", and for an assignment I need to simplify the following, leaving my answer as a single base raised to a single exponent:

    9^2 * 12^3 * 2

    I can't seem to find the steps needed to get the answer which is supposed to be 6^7. Normally I would look for common bases (like 9 and 27 have 3 in common), but I don't see that in 9 and 12.

    Can someone explain this to me?
    Hint: 9=3^2 and 12=3\cdot 2^2
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  3. #3
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    Re: Multiplying different bases with different exponent

    Ah now i see. Thanks.

    (3^2)^2 * (3*2^2)^3
    => 3^4 * 3^3 * 2^6 * 2
    => 3^7 * 2^7
    => 6^7

    That must be it, right?
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Re: Multiplying different bases with different exponent

    Quote Originally Posted by timmeh View Post
    Ah now i see. Thanks.

    (3^2)^2 * (3*2^2)^3
    => 3^4 * 3^3 * 2^6 * 2
    => 3^7 * 2^7
    => 6^7

    That must be it, right?
    Yup!
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