With the exception of resistance mixers, all mixers with built-in effects are powered. However, the output is measured in milli-watts (mW). And, if I recall correctly, the output sound levels these types of mixers are measured in Decibel Units (dBu). While there's insufficient wattage to power speakers, they're still powered. Additionally, they require a voltage source for the processor and pre-amplification circuitry.
In the case of resistance mixers, they are merely a series of parallel inputs that connect to a single output. The only thing they can do is to lower the signals fired through the inputs, which in the case of mics and guitar pickups, is very small. The DOD-240
Resistance mixer is a classic example of this.
And, it is listed as an unpowered mixer.
The product you seem to be referring to is a mixer/amp, which is a combination of a powered mixer and amplifier. With those, you can bypass the amplifier section by merely outputting from the line-out.
Just a difference in interpretation of terminology. I gotta' start drinkin' more Kickapoo Joy Juice!
Gary
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Travlin' Easy