What does the label on the device say? It should give you the voltage and the amp-draw of the equipment, and this would tell you the wire-gauge required to drive it as per the Uniform Electrical Code tables.
To run the 15-amp load that I see on most online catalog entries for "Furman power conditioners," a 14-gauge extension cord is probably minimum (for runs of less than 50 feet), but, y'know, I'd just splurge and go on up to 12. (The difference in cost is negligible. But also, 16-gauge is not listed as code-adequate for 15 amps.)
But of course, the amount of power that it actually will draw should be determined by the total of what you attach to it. Check the specs of each attached device.
Also, make sure that the associated socket is connected to a breaker of the proper capacity (considering what else is also on the same line), and that the ground connection is actually attached to anything (heh ...), and attached to a good earth ground. Meters which can tell you the actual quality and characteristics of any plug are well worth the money – can explain many "mysterious" problems – and any electrician can quickly help you add a high-quality ground if necessary.
I know that some musicians have had electricians install separate dedicated circuits for their studio, with their own separate earth grounding-stake, to avoid "cross-talk" and noise in the ground connection, e.g. when a dishwasher or a clothes dryer kicks in or out.
High-quality, clean electrical power is vital. I've also had several people tell me that they ran one circuit for "digital" and an entirely separate one for "analog." May have used two grounding-stakes, too.
"I wanna quit being a computer consultant and become a composer and arranger at age fifty-nevermind."
Logic Pro X, MacBook Pro, 88-key MIDI controller.
Just south of Chattanooga, Tennessee, USA