Do the powered speakers (what brand and model are they) have balanced inputs. There is a way of wiring from unbalanced out (nano Patch) to balanced in that sometimes eliminates noise. It requires you to make a special lead. It might work in your case but you need a proper balanced input for this to work.
For example when I connect a stereo mini jack out (IMac) or most computers to two line inputs on my digital mixer (even though my line inputs are balanced) using the normal approach of unbalancing one side of the balanced input, I sometimes get high freq noise like you are describing.
I have made a special lead now that connects to the balanced line inputs (not using the normal sleeve earth that is) and this noise is not present when I do it this way. It may work in your case too.