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Math Help - Fractional Powers

  1. #1
    Junior Member
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    Fractional Powers

    Hi,

    I did a non-calculator past paper and I got to this answer:

    25 (〖1/5)〗^9

    however when I had checked the mark scheme the answer that was given was simplified further (and worth an extra mark) to:

    1.28*10^-5

    How can I get to that answer by hand?
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, CSG18

    I did a non-calculator past paper and I got to this answer:

    . . 25 \times \left(\frac{1}{5}\right)^9

    However, the answer given was simplified further (and worth an extra mark) to:

    . . 1.28 \times 10^{-5}


    How can I get to that answer by hand?
    By hand? . . . ack!


    We have:. 5^2 \times \frac{1}{5^9} \;=\;\frac{1}{5^7}

    Then: . \left(\frac{1}{5}\right)^7 \;=\;(0.2)^7 \;=\;\left(2\times 10^{-1}\right)^7 \;=\;2^7 \times \left(10^{-1}\right)^7 \;=\;128 \times 10^{-7} \;=\;1.28 \times 10^{-5}

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  3. #3
    Junior Member
    Joined
    Feb 2010
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    Thanks Soroban!

    That is a good way to reach that answer - very straight forward.

    Thanks again.
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