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Math Help - A quick algebra exercise

  1. #1
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    A quick algebra exercise

    3^{x+1} + 3^{x+2}

    How do I simplify this?
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  2. #2
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by klik11 View Post
    3^{x+1} + 3^{x+2}

    How do I simplify this?


     3^{x+1} + 3^{x+2 } = 3 \cdot 3^x + 3^2 \cdot 3^x = 3^x ( 3 + 3^2 ) = 3^x \cdot (3+9 ) = 3^x \cdot 12
    Last edited by yeKciM; September 13th 2010 at 04:08 AM.
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  3. #3
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    I'm Sorry, I forgot to say that the book says that the answer is
    12*3^{x}

    Could you show me the way to get to that answer?

    Edit: I also think you are wrong because it would have been your answer if it there was * and not +.
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  4. #4
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by klik11 View Post
    I'm Sorry, I forgot to say that the book says that the answer is
    12*3^{x}

    Could you show me the way to get to that answer?
    thank you ... lol sorry working so many things at the same time .... I edited that one up there
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  5. #5
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    Could you explain me how come

    3 \cdot 3^x + 3^2 \cdot 3^x = 3^x ( 3 + 3^2 )
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  6. #6
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by klik11 View Post
    Could you explain me how come

    3 \cdot 3^x + 3^2 \cdot 3^x = 3^x ( 3 + 3^2 )
    okay ...

     3^2 = 3^1 \cdot 3^1

    so

     3^{x+1} = 3^x \cdot 3^1

    now you can write

     3 \cdot 3^x + 3^2 \cdot 3^x

    here you see both of them have common  3^x so you can pull it out ...

     yx +2x = x (y+2 )

    same thing

     3 \cdot 3^x + 3^2 \cdot 3^x = 3^x ( 3 + 3^2 )
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  7. #7
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    Remember that a^x * a^y = a^(x+y) and (a^x)^y = a^(xy)
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