SOLUTION: Square root of a to the 5th, inside cube root of whole thing?

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Question 616408: Square root of a to the 5th, inside cube root of whole thing?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
root%283%2C+sqrt%28a%5E5%29%29
The simplest way to simplify this is to rewrite the radicals as fractional exponents. Square roots can be replaced with exponents of 1/2, code rotts with 1/3, 4th roots with 1/4, etc.
%28%28a%5E5%29%5E%281%2F2%29%29%5E%281%2F3%29
Now we can use our exponent rule for a power of a power: Multiply the exponents. Starting from the inside:
%28a%5E%28%285%2A%281%2F2%29%29%29%29%5E%281%2F3%29
%28a%5E%285%2F2%29%29%5E%281%2F3%29
a%5E%28%28%285%2F2%29%2A%281%2F3%29%29%29
a%5E%285%2F6%29
This may be an acceptable answer. But if you want an answer in radical form we can use: x%5E%28p%2Fq%29+=+root%28q%2C+x%5Ep%29 (or %28root%28q%2C+x%29%29%5Ep) to change a%5E%285%2F6%29 to
root%286%2C+a%5E5%29 (or %28root%286%2C+a%29%29%5E5)