SOLUTION: Please help me simplify this: 6th root of 256. I get 2 times the 6th root of 4; however, the book answer is 2 times the third root of 2 sorry, I don't know how to put th

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me simplify this: 6th root of 256. I get 2 times the 6th root of 4; however, the book answer is 2 times the third root of 2 sorry, I don't know how to put th      Log On


   

Question 1012129: Please help me simplify this:
6th root of 256.
I get 2 times the 6th root of 4; however, the book answer is 2 times the third root of 2
sorry, I don't know how to put the math symbols in this application. Thank you in advance for the help.

Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
256^(1/6)
=16^2^(1/6)=16^(1/3)
={4^2}^1/3
=4^(2/3)
={2^2}^(2/3)
=2^(4/3)
=2^(3/3)*2^(1/3)
=2*2(1/3), which is what you want.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Please help me simplify this:
6th root of 256.
I get 2 times the 6th root of 4; however, the book answer is 2 times the third root of 2
sorry, I don't know how to put the math symbols in this application. Thank you in advance for the help. 
root+%286%2C+256%29 ------> root+%286%2C+2%5E8%29 -----> root+%286%2C+2%5E6+%2A+2%5E2%29 ------> 2+%2A+root+%28cross%286%29%2C+cross%282%5E6%29+%2A+2%5E2%29 ------> highlight_green%282+%2A+root+%286%2C+2%5E2%29%29 <-------> This is what you got, which is correct. The thing though, is that:

root+%286%2C+2%5E2%29 is the same as: highlight%28highlight%282%5E%281%2F3%29%29%29, and highlight%28highlight%282%5E%281%2F3%29%29%29 is the same as: root+%283%2C+2%29. Therefore, highlight_green%282+%2A+root+%286%2C+%282%5E2%29%29%29 is: highlight_green%282+%2A+root+%283%2C+2%29%29