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Math Help - exponent problems

  1. #1
    Member garymarkhov's Avatar
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    exponent problems

    Is it possible that Y=A(tY)^{1-\alpha}K^{\alpha} is equivalent to Y=A^\frac{1}{\alpha}t^\frac{1-\alpha}{\alpha}K ? Where the heck did the Y that was on the right hand side go??
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  2. #2
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    Quote Originally Posted by garymarkhov View Post
    Is it possible that Y=A(tY)^{1-\alpha}K^{\alpha} is equivalent to Y=A^\frac{1}{\alpha}t^\frac{1-\alpha}{\alpha}K ? Where the heck did the Y that was on the right hand side go??
    Y = At^{1-\alpha}Y^{1-\alpha}K^{\alpha}

    \frac{Y}{Y^{1-\alpha}} = At^{1-\alpha}K^{\alpha}

    Y^{\alpha} = At^{1-\alpha}K^{\alpha}

    (Y^{\alpha})^{\frac{1}{\alpha}} = (At^{1-\alpha}K^{\alpha})^{\frac{1}{\alpha}}

    Y=A^\frac{1}{\alpha}t^\frac{1-\alpha}{\alpha}K
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  3. #3
    Member garymarkhov's Avatar
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    Quote Originally Posted by skeeter View Post
    Y = At^{1-\alpha}Y^{1-\alpha}K^{\alpha}

    \frac{Y}{Y^{1-\alpha}} = At^{1-\alpha}K^{\alpha}

    Y^{\alpha} = At^{1-\alpha}K^{\alpha}

    (Y^{\alpha})^{\frac{1}{\alpha}} = (At^{1-\alpha}K^{\alpha})^{\frac{1}{\alpha}}

    Y=A^\frac{1}{\alpha}t^\frac{1-\alpha}{\alpha}K
    That's fantastic.
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