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.  
<pre>{{{root (6, 256)}}} ------> {{{root (6, 2^8)}}} -----> {{{root (6, 2^6 * 2^2)}}} ------> {{{2 * root (cross(6), cross(2^6) * 2^2)}}} ------> {{{highlight_green(2 * root (6, 2^2))}}} <-------> This is what you got, which is correct. The thing though, is that:
{{{root (6, 2^2)}}} is the same as: {{{highlight(highlight(2^(1/3)))}}}, and {{{highlight(highlight(2^(1/3)))}}} is the same as: {{{root (3, 2)}}}. Therefore, {{{highlight_green(2 * root (6, (2^2)))}}} is: {{{highlight_green(2 * root (3, 2))}}}