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Math Help - Exponents and square roots

  1. #1
    Junior Member
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    Exponents and square roots

    For the question :

    The square root of the fifth root of 4a^4

    is the answer:

    2^\frac15a^\frac25

    that was the answer in my book and i do not understand how to get it.
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  2. #2
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    \sqrt {\sqrt[5]{{4a^4 }}}  = \left( {\left( {4a^4 } \right)^{\frac{1}{5}} } \right)^{\frac{1}{2}}  = \left( {\left( {4a^4 } \right)^{\frac{1}{2}} } \right)^{\frac{1}{5}}  = \left( {2a^2 } \right)^{\frac{1}{5}}  = \left( {2^{\frac{1}{5}} } \right)\left( {a^{\frac{2}{5}} } \right)<br />
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