Simplify. 
    ____
3[³Öx5y5]

Prime factor what's under the cube root radical:
    ___________________
3[³Öx·x·x·x·x·y·y·y·y·y]

Since it's cube root (index 3), group like factors 
into groups of 3 each:

    _______________________
3[³Ö(x·x·x)·x·x·(y·y·y)·y·y]

Each group of three is a perfect cube, and so each
comes out in front of the radical as a single factor
That is the (x·x·x) is x3 and so it comes out in front
of the radical as a single x.  Same for (y·y·y).  The
factors that didn't get grouped stay under the radical:

        _______
3·x·y·³Öx·x·y·y
 
Simplify
      ____
3xy·³Öx2y2

Edwin