1. Connect the microphone directly into your powered speaker's mic input.
This method definitely achieves the desired results of assuring that your microphone plays in full-range mono, and allows everybody to be heard very well. But logistically, it does not provide the most ideal circumstances.
You're a sound engineer. That means you will be constantly alert to tweak levels if necessary. Having to reach high up on your speaker stand to adjust the mic, and then turn back to your table to run the music, could get very old, pretty quickly.
You will want to keep everything as centralized, on your table, as possible. But if you do apply this method (in a pinch, it can really come in handy) make sure that your speaker's input switch (if connecting to a dual-level jack) is on "mic," and not "line."
2. Connect to your mixer's mono output jack.
If your mixer has a secondary mono output jack, then connecting your powered speaker to it will achieve your desired results.
3. Turn your mixer's stereo/mono switch to mono.
Just like a dedicated mono output jack, not all mixers have a stereo/mono switch. But if your mixer does, you will achieve success by putting it on mono when connecting to only the left, or the right, main output jack of your mixer.
4. Pan your mixer's microphone input channel.
Panning is a fancy industry term for turning the microphone's balance (which should be labeled "pan" on your mixer) completely to the left, or completely to the right.
When you're connecting your speaker to only the left, or right, main output jack of a mixer without a stereo/mono switch, turn the microphone's "pan" control to the appropriate position.
5. Employ splitter cables
In these cases, the end connecting to your mixer will have two plugs, so you can connect to both the left and right output channels on your mixer. When connecting the other end to your powered speaker, 1/8 inch stereo and/or XLR plugs will fit into one socket, while RCA jacks will have two (one for the left, and one for the right).
1/8 inch stereo input jacks are intended for MP3 players, and are typically pre-amplified accordingly. Please keep this in mind when adjusting your levels, if you plan to use this option.
As of this writing, 1/4 inch input sockets on powered speakers are not stereo-compatible. So even if the 1/4 inch end of your adapter is stereo, you will typically only hear the left channel. Panning your mixer's mic input back & forth is the best way to find out.