SOLUTION: I need help ASAP PLEASE!!! I need to simplify {{{root(4,(3x^5)/(81y^3))}}} Thank you so much!

Let's break everything down into primes:



Since the index is 4, we need to get all the groups of 4
like factors that we can.  So we'll group 
and  in parentheses:



and replace  by 

and replace  by  



But we need another  factor in the bottom
so that we will have only groups of 4 like factors
in the denominator. So we multiply top and bottom
by another 



Now we can also group the 4 's



Now we replace  by 



Now when we take the 4th root of a 4th power
we take away the 4th root radical and the 4
exponent. That is we take them out of the 
radical.



Notice we take the entire denominator out of the
radical, so there is no denominator left under the
radical.  The only thing left under the radical
are those factors left over after we grouped into
4's.

Edwin