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Math Help - Simplifying some algebraic exponent expressions

  1. #1
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    Simplifying some algebraic exponent expressions

    Question 1:

    \frac{\sqrt[10]{1024x^{20}}}{\sqrt[9]{512x^{27}}}

    =\frac{1024x^{\frac{20}{10}}}{512x^{\frac{27}{9}}}

    =\frac{1024x^{\frac{2}{1}}}{512x^{\frac{3}{1}}}

    =2x^{-1}

    =\frac{2}{x}

    Textbook answer:

    \frac{1}{x}


    Question 2:

    \frac{\sqrt[6]{(8x^{6})^2}}{\sqrt[4]{625x^{8}}}

    =\frac{\sqrt[6]{64x^{12}}}{\sqrt[4]{625x^{8}}}

    =\frac{64x^{\frac{12}{6}}}{625x^{\frac{8}{4}}}

    =\frac{64}{625}

    Textbook answer:

    \frac{2}{5}


    Does anyone know where I made the errors?
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by RogueDemon View Post
    Question 1:

    \frac{\sqrt[10]{1024x^{20}}}{\sqrt[9]{512x^{27}}}

    =\frac{1024x^{\frac{20}{10}}}{512x^{\frac{27}{9}}}

    =\frac{1024x^{\frac{2}{1}}}{512x^{\frac{3}{1}}}

    =2x^{-1}

    =\frac{2}{x}

    Textbook answer:

    \frac{1}{x}




    Question 2:

    \frac{\sqrt[6]{(8x^{6})^2}}{\sqrt[4]{625x^{8}}}

    =\frac{\sqrt[6]{64x^{12}}}{\sqrt[4]{625x^{8}}}

    =\frac{64x^{\frac{12}{6}}}{625x^{\frac{8}{4}}}

    =\frac{64}{625}

    Textbook answer:

    \frac{2}{5}


    Does anyone know where I made the errors?
    1.

    \frac{\sqrt[10]{1024x^{20}}}{\sqrt[9]{512x^{27}}}

    = \frac{1024^{\frac{1}{10}}x^{\frac{20}{10}}}{512^{\  frac{1}{9}}x^{\frac{27}{9}}}

    = \frac{(2^{10})^{\frac{1}{10}}x^{\frac{20}{10}}}{(2  ^9)^{\frac{1}{9}}x^{\frac{27}{9}}}

    = \frac{2x^2}{2x^3}

    = \frac{x^2}{x^3}

    Do the same for the second problem
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  3. #3
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    simplifying expressions

    Quote Originally Posted by RogueDemon View Post
    Question 1:

    \frac{\sqrt[10]{1024x^{20}}}{\sqrt[9]{512x^{27}}}

    =\frac{1024x^{\frac{20}{10}}}{512x^{\frac{27}{9}}}

    =\frac{1024x^{\frac{2}{1}}}{512x^{\frac{3}{1}}}

    =2x^{-1}

    =\frac{2}{x}

    Textbook answer:

    \frac{1}{x}


    Question 2:

    \frac{\sqrt[6]{(8x^{6})^2}}{\sqrt[4]{625x^{8}}}

    =\frac{\sqrt[6]{64x^{12}}}{\sqrt[4]{625x^{8}}}

    =\frac{64x^{\frac{12}{6}}}{625x^{\frac{8}{4}}}

    =\frac{64}{625}

    Textbook answer:

    \frac{2}{5}


    Does anyone know where I made the errors?

    in the first the numbers must show new exponents like 1024^1/10.when you make the corrections the answer is 1/x.Follow the same way in the second.


    bjh
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