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Math Help - exponents

  1. #1
    Cals
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    Exclamation exponents

    please help with this kind of sum

    n+1 2n-1
    12 x 9
    n 1-n
    36 x 8
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Cals View Post
    please help with this kind of sum

    n+1 2n-1
    12 x 9
    n 1-n
    36 x 8
    i'm not quite sure what is going on here. do you mean

    \frac {12^{n+1} \cdot 9^{2n - 1}}{36^{n} \cdot 8^{1-n}} ?

    the dots mean multiply
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  3. #3
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    Hello, Cals!

    I must assume you know the basic Exponent Rules . . .


    \frac{12^{n+1}}{36^n}\cdot\frac{9^{2n-1}}{8^{1-n}}
    Note that all the numbers are made up of 2's and 3's . . .


    We have: . \frac{(2^2\!\cdot\!3)^{n+1}\cdot(3^2)^{2n+1}}{(2^2  \!\cdot\!3^2)^n\cdot(2^3)^{1-n}} \;=\;\frac{(2^2)^{n+1}\cdot(3)^{n+1}\cdot(3)^{2(2n  +1)} }{(2^2)^n\cdot(3^2)^n\cdot(2)^{3(1-n)}} \;=\;\frac{2^{2n+2}\cdot3^{n+1}\cdot3^{4n+2}} {2^{2n}\cdot3^{2n}\cdot2^{3-3n}}

    Multipfy (add exponents): . \frac{2^{2n+2}\cdot3^{5n+3}}{2^{3-n}\cdot3^{2n}}

    Divide (subtract exponents): . \boxed{2^{3n-1}\!\cdot\!3^{3n+3}}

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