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Math Help - Intergers and Eponents

  1. #1
    Newbie Kitty_Kat's Avatar
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    Exclamation Intergers and Eponents

    Please tell me the steps to get through these questions;

    1) (8.9x10 to the exponent 5) to the exponent 4

    2) (4x10 the the eponent negative 5) to the exponent negative 6

    3) (6x10 to the exponent negative 5) to the exponent 3

    All help is greatly appreciated.
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  2. #2
    Member Ranger SVO's Avatar
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    1. 890,000 and 89,000
    See a pattern, simply move the decimal to the right 5 places for the first one or 4 places for the second one

    2. 0.00004 and 0.000004
    now we move the decimal place to the left 5 places for the first one and 6 places for the second one.

    negative exponent move left
    posite exponent move right

    Bet you can get the next one.
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  3. #3
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by Kitty_Kat View Post
    Please tell me the steps to get through these questions;

    1) (8.9x10 to the exponent 5) to the exponent 4

    2) (4x10 the the eponent negative 5) to the exponent negative 6

    3) (6x10 to the exponent negative 5) to the exponent 3

    All help is greatly appreciated.
    You need to know this property: \left(x^a\right)^b=x^{(ab)}

    So: \left(8.9\times10^5\right)^4=8.9\times10^{(5\times  4)}=8.9\times10^{20}

    EDIT: Wow, I completely forgot to distribute the exponent
    Last edited by Quick; December 28th 2006 at 04:20 AM.
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  4. #4
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    Hello, Kitty_Kat!

    You didn't give us any instructions.
    I will assume the answers are to be in Scientific Notation.


    1)\;\;\left(8.9 \times 10^5\right)^4
    \left(8.9 \times 10^5\right)^4\;=\;8.9^4 \times \left(10^5\right)^4 \;=\;6,274.2241 \times 10^{20} \;=\;6.2742241 \times 10^{23}


    2)\;\;\left(4 \times 10^{-5}\right)^{-6}
    \left(4\times10^{-5}\right)^{-6}\;=\;4^{-6}\times\left(10^{-5}\right)^{-6} \;=\;0.000244140625 \times 10^{30}\;=\;2.44140625 \times 10^{26}


    3)\;\;\left(6 \times 10^{-5}\right)^3
    \left(6\times10^{-5}\right)^3\;=\;6^3\times\left(10^{-5}\right)^3\;=\;216\times10^{-15}\;=\;2.16\times10^{-13}
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