Exponents and square roots

**t-dot** · October 20th 2007, 02:22 PM

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.

**Plato** · October 20th 2007, 02:46 PM

$\sqrt {\sqrt[5]{{4a^4 }}} = \left( {\left( {4a^4 } \right)^{\frac{1}{5}} } \right)^{\frac{1}{2}} = \left( {\left( {4a^4 } \right)^{\frac{1}{2}} } \right)^{\frac{1}{5}} = \left( {2a^2 } \right)^{\frac{1}{5}} = \left( {2^{\frac{1}{5}} } \right)\left( {a^{\frac{2}{5}} } \right)<br />$

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