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  1. #1
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    Simplify

    Simplify using the law of rational exponents?

    1)√8c^8
    2)^5√-96x^25y^12
    3)√40r^5t^3s^8

    please answer in steps
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  2. #2
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    Quote Originally Posted by mj.alawami View Post
    Simplify using the law of rational exponents?

    1)√8c^8
    2)^5√-96x^25y^12
    3)√40r^5t^3s^8

    please answer in steps
    Hi mj,

    1) \sqrt[3]{8c^8}=\sqrt[3]{2^3c^3c^3c^2}=2c\cdot c\sqrt[3]{c^2}=2c^2\sqrt[3]{c^2}

    Using rational exponents:

    (2^3)^{1/3}c^{8/3}=2c^{8/3}
    Last edited by masters; January 29th 2009 at 09:30 AM.
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    Quote Originally Posted by mj.alawami View Post
    Simplify using the law of rational exponents?

    1)√8c^8
    2)^5√-96x^25y^12
    3)√40r^5t^3s^8

    please answer in steps
    3) \sqrt{40r^5t^3s^8}=\sqrt{4 \cdot 10 \cdot r^4 \cdot r \cdot t^2 \cdot t \cdot s^8}=2r^2s^4t\sqrt{10rt}

    Using rational exponents:

    \sqrt{40r^5t^3s^8}=\sqrt{4 \cdot 10 \cdot r^5 \cdot t^3 \cdot s^8}=(2^2)^{1/2}\cdot 10^{1/2} \cdot r^{5/2} \cdot t^{3/2} \cdot s^{8/2}=2 \cdot 10^{1/2} \cdot r^{5/2} \cdot t^{3/2} \cdot s^4
    Last edited by masters; January 29th 2009 at 09:44 AM.
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    Quote Originally Posted by masters View Post
    Hi mj,

    1) \sqrt[3]{8c^8}=\sqrt[3]{2^3c^3c^3c^2}=2c\cdot c\sqrt[3]{c^2}=2c^2\sqrt[3]{c^2}
    Can my simplifying be

    2c^8/3
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  5. #5
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    Quote Originally Posted by mj.alawami View Post
    Simplify using the law of rational exponents?

    1)√8c^8
    2)^5√-96x^25y^12
    3)√40r^5t^3s^8

    please answer in steps
    I'm going to guess that you mean this:

    2) \sqrt[5]{-96x^{25}y^{12}}=\sqrt[5]{-32 \cdot 3 \cdot x^{25} \cdot y^{12}}=-2x^5y^2\sqrt[5]{3y^2}

    Using rational exponents:

    \sqrt[5]{-96x^{25}y^{12}}=\sqrt[5]{-32 \cdot 3 \cdot x^{25} \cdot y^{12}}=-2 \cdot 3^{1/5}x^5y^{12/5}
    Last edited by masters; January 29th 2009 at 09:41 AM.
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    Quote Originally Posted by mj.alawami View Post
    Can my simplifying be

    2c^8/3
    Sorry mj,

    I failed to read your initial instructions. You want to use rational exponents not radicals. You are correct for your first one. I will redo my post so that it uses rational exponents.
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    [quote=mj.alawami;256717]

    Is the second answer:-
    -2* ^5√3 * x^5 * y^2 ^5√y^2
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    Quote Originally Posted by masters View Post
    Sorry mj,

    I failed to read your initial instructions. You want to use rational exponents not radicals. You are correct for your first one. I will redo my post so that it uses rational exponents.
    hey,dont bother about me i will get it ,by the way thank you for taking the time to read my question
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    [quote=mj.alawami;256724]
    Quote Originally Posted by mj.alawami View Post

    Is the second answer:-
    -2* ^5√3 * x^5 * y^2 ^5√y^2
    mj,

    I don't think you want to mix radicals and rational exponents. I have modified my posts to show rational exponents. Have a look. See if you have any questions about them.
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  10. #10
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    [quote=masters;256738]
    Quote Originally Posted by mj.alawami View Post

    mj,

    I don't think you want to mix radicals and rational exponents. I have modified my posts to show rational exponents. Have a look. See if you have any questions about them.
    Thank you very much ,you really have helped me alot and no more question for today X|
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