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Math Help - help with radical exponents

  1. #1
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    help with radical exponents

    3 root (x ^2 y ^ 5) ^ 12 how do i write that as a single radical expression?
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    Quote Originally Posted by diehardmath4 View Post
    3 root (x ^2 y ^ 5) ^ 12 how do i write that as a single radical expression?

    Hello diehardmath4,

    If I translated your code correctlly, there is no radical.

    \sqrt[3]{(x^2y^5)^{12}}=(x^2y^5)^4=x^8y^{20}
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    can you please explain it a little further because i'm having a bit of trouble breaking down the steps
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    Quote Originally Posted by diehardmath4 View Post
    can you please explain it a little further because i'm having a bit of trouble breaking down the steps

    \sqrt[3]{(x^2y^5)^{12}}=(x^2y^5)^{\frac{12}{3}}=(x^2y^5)^4  =x^8y^{20}

    Recall this:

    \sqrt[n]{a^m}=a^{\frac{m}{n}}

    And maybe this, too:

    (x^ay^b)^n=x^{an}y^{bn}
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  5. #5
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    More on Radicals

    x ^ 8 / 15 y 7 / 15
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    x^1/3 y ^ - 1 / 5

    I got x ^ 3 y 8 is that correct ?
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    Quote Originally Posted by diehardmath4 View Post
    x ^ 8 / 15 y 7 / 15
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    x^1/3 y ^ - 1 / 5

    I got x ^ 3 y 8 is that correct ?
    Actually, I got something different when I subtracted your exponents:

    \frac{8}{15}-\frac{1}{3}=\frac{1}{5}

    \frac{7}{15}-\frac{-1}{5}=\frac{2}{3}


    \dfrac{x^{\frac{8}{15}}y^{\frac{7}{15}}}{x^{\frac{  1}{3}}y^{-\frac{1}{5}}}=x^{\frac{1}{3}}y^{\frac{2}{3}}
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