SOLUTION: the fourth root of 49u^14..........simplify by first converting to rational expression..

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Question 253231: the fourth root of 49u^14..........simplify by first converting to rational expression..
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We start with fourth root (49*u^14).
We can rewrite this in fractional exponent form as
(i) %2849u%5E14%29%5E%281%2F4%29
Now, we are looking for groups of 4 in order to pull out one set. So I will expand (i) to get
(ii) 7%2A7%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au
Now I look for groups of four. I get
(iii) 7%2A7%2A%28u%2Au%2Au%2Au%29%2A%28u%2Au%2Au%2Au%29%2A%28u%2Au%2Au%2Au%29%2Au%2Au
I see 3 groups of 4 u's, so I can take out the 3 groups as u^3. Nothing else comes out, so we are left with the answer as:
--
u%5E3%2A%287%2A7%2Au%2Au%29%5E%281%2F4%29
or
u%5E3%2A%2849u%5E2%29%5E%281%2F4%29