The short answer is: It depends on the tool and you "should" unplug the refrigerator to prevent an overload if the refrigerator should happen to "cycle on" while the tool is in use.
Most residential refrigerators are connected with a 1000 watt inverter. 1000 watts at 120 VAC is 8.3 amps. Very few power tools are rated at 8 amps. Most are rated well over 10 amps and many are rated at 15+ amps. So, it depends on which tool you use and whether you want to go through the hassle of protecting your refrigerator while using the tool ..... Remember, when reading the amperage use for the tool, use the "higher number" which is the starting amperage.
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John
2015 F250 6.7l 4x4
2014 Cougar X Lite 27RKS
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