SOLUTION: Use rational exponents to simplify. Write the answer in radical notation, if possible {{{root(6,a^4)}}}

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Question 160539: Use rational exponents to simplify. Write the answer in radical notation, if possible
root%286%2Ca%5E4%29


Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

root%286%2Ca%5E4%29

Use the definition rule:  root%28N%2CX%5EM%29=X%5E%28M%2FN%29

root%286%2Ca%5E4%29=a%5E%284%2F6%29

But then we can reduce the fraction exponent 4%2F6 to 2%2F3

root%286%2Ca%5E4%29=a%5E%284%2F6%29=a%5E%282%2F3%29

Now use the above definition rule in reverse X%5E%28M%2FN%29=root%28N%2CX%5EM%29
to get it back to a radical:

root%286%2Ca%5E4%29=a%5E%284%2F6%29=a%5E%282%2F3%29=root%283%2Ca%5E2%29

Edwin