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Math Help - Simplifying an expression involving indices

  1. #1
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    Question Simplifying an expression involving indices

    I know that:

    (7^{x+2}(-9)^{x+2}) = (-63)^{x+2}

    My brain appears to be shutting down as to the reason why, I think the rule is:

     x^m y^m = xy^m

    but this one is not in the textbook. If this is right any chance someone could explain why it is right (being a bit dizzy tonight).

    Thanks in advance,

    Alice
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by AliceFisher View Post
    I know that:

    (7^{x+2}(-9)^{x+2}) = (-63)^{x+2}

    My brain appears to be shutting down as to the reason why, I think the rule is:

     x^m y^m = xy^m

    but this one is not in the textbook. If this is right any chance someone could explain why it is right (being a bit dizzy tonight).

    Thanks in advance,

    Alice
    This is not a rule. The actual rule is x^my^m = (xy)^m


    7^{x+2} \times -9^{x+2} - using the rule above (since you have the same exponent) you get (7 \times -9)^{x+2} = -63^{x+2}


    Since this is the correct answer I'm guessing you copied the rule down wrong
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  3. #3
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    Thanks e^(i*pi),

    I was sure that was the right answer but I was starting to doubt myself since I could not find the rule in my head or your corrected rule in the textbook. This means my final answer is right which means I can go to sleep now.
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