The simplest and cheapest way would be to run a 3.5mm stereo mini to RCA cable from the headphone jack to the powered speakers.
The jack is actually a dual output jack, headphone and digital optical, so for better quality you could get a digital to analog converter (DAC) with optical input and use a mini-Toslink to Toslink cable to the DAC, then use its RCA outputs with a standard RCA cable to the speakers.
The jack is actually a dual output jack, headphone and digital optical, so for better quality you could get a digital to analog converter (DAC) with optical input and use a mini-Toslink to Toslink cable to the DAC, then use its RCA outputs with a standard RCA cable to the speakers.