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Math Help - high school algebra problem

  1. #1
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    high school algebra problem

    Having some trouble with this one.

    My understanding so far is that if  x^-1 then it equals  1/x. Also that  x^1/2 equals  sqrt x.

    The problem I am trying to simplify is (81/16)^-3/4.

    I have simplified it to 4sqrt (16/81)^3

    Can someone help me in the right direction please?

    Not sure what the code for square root is in the math writing program either :S
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  2. #2
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    Quote Originally Posted by smplease View Post
    Having some trouble with this one.

    My understanding so far is that if  x^-1 then it equals  1/x. Also that  x^1/2 equals  sqrt x.

    The problem I am trying to simplify is (81/16)^-3/4.

    I have simplified it to 4sqrt (16/81)^3

    Can someone help me in the right direction please?

    Not sure what the code for square root is in the math writing program either :S
    \left(\frac{81}{16}\right)^{-\frac{3}{4}} =

    \left(\frac{16}{81}\right)^{\frac{3}{4}} =

    \left[\left(\frac{2^4}{3^4}\right)^{\frac{1}{4}}\right]^3 =

    \left(\frac{2}{3}\right)^3 = \frac{8}{27}
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by smplease View Post
    Having some trouble with this one.

    My understanding so far is that if  x^-1 then it equals  1/x. Also that  x^1/2 equals  sqrt x.

    The problem I am trying to simplify is (81/16)^-3/4.

    I have simplified it to 4sqrt (16/81)^3

    Can someone help me in the right direction please?

    Not sure what the code for square root is in the math writing program either :S
    see here for instructions on using LaTeX, the markup language built into the forum through which you can get pretty math symbols

    Now, note that \left( \frac ab \right)^n = \frac {a^n}{b^n} and \left( \frac ab \right)^{-n} = \frac 1{\left( \frac ab \right)^n} = \left( \frac ba \right)^n

    So, then

    \left( \frac {81}{16} \right)^{-3/4} = \left( \frac {16}{81} \right)^{3/4}

    = \frac {16^{3/4}}{81^{3/4}}

    = \frac {( \sqrt[4]{16})^3}{(\sqrt[4]{81})^3}

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

    = \frac 8{27}
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  4. #4
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    thanks for that guys
    the 3/4 was throwing me off
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