SOLUTION: how to write an equivalent expression using radical notation for (16a^6)^3/4

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Question 274702: how to write an equivalent expression using radical notation for
(16a^6)^3/4
Found 3 solutions by stanbon, jim_thompson5910, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
how to write an equivalent expression using radical notation for
(16a^6)^3/4
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4th root of (16a^6)^3
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Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that x%5E%28m%2Fn%29%5E%22%22=root%28n%2Cx%5Em%29


This means that %2816a%5E6%29%5E%283%2F4%29%5E%22%22=root%284%2C%2816a%5E6%29%5E3%29


We could optionally cube 16a%5E6 to get 4096a%5E18 which would mean that %2816a%5E6%29%5E%283%2F4%29%5E%22%22=root%284%2C4096a%5E18%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
how to write an equivalent expression using radical notation for
(16a^6)^3/4
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= (2^4*a^6)^(3/4)
= sqrt%28sqrt%282%5E12%2Aa%5E18%29%29
=sqrt%282%5E6%2Aa%5E9%29
= 2%5E3%2Aa%5E4%2Asqrt%28a%29
= 8a%5E4%2Asqrt%28a%29