This is not about power it is about the bass signal coming from each channel of your amplifier. You have bass signals coming from both the right and left channel of your amplifier. If you just take the signal from the left side of your amplifier, you will only get the bass signal from your left channel of the amplifier, and any bass signal coming from the right channel will not go to your subwoofer, but only to you regular speakers.

This particular subwoofer allows for you to run your full right and left channel output from your amplifier to the subwoofer and the crossover in the subwoofer will sort out only the low frequencies to go to the subwoofer. It will eliminate any frequencies above where you set the crossover frequencies going to the subwoofer, thereby allowing the subwoofer to only handle the frequencies it is meant to handle. The splitter is needed to take the right and left channel signals and send one signal to the subwoofer and another signal to the regular speakers. If you also know the low frequencies your regular speakers go down to (for these speakers that is about 110 htz, and the subwoofer covers frequencies from around 40 htz to 150 htz) then you would likely sent the subwoofer low pass filter at about 110 to 150 htz to cover the frequencies that the right and left speakers do not cover. You could also do the same thing by just buying some extra speaker wire and running two pairs of wire from both the right and left channels of your amplifier. Run one set to the subwoofer and the other set to the regular speakers. This subwoofer has both types of hookups available, so it is your choice. Use the same frequencie settings with the low pass filter with this hookup as well.

Hope this helped and did not just confuse the issue even more.