Follow the numbers
A 1,000 Watt microwave (cooking power) pulls about 1,500 Watts of electricity. Even if inverter is relatively inefficient, battery bank will have to supply inverter with no more than 2,000 Watts (about 170 Amps). If an RV had 8 batteries (say around 800 Amp-hours) as mentioned above, there should be no problem running a microwave for a few minutes to heat coffee, make hot chocolate, or even to cook a TV dinner for 5 minutes or longer. I know guys powering smaller van-size 700-Watt microwaves with only two batteries.
However, with exception of a few motorhomes that are providing inverter-electric capabilities in lieu of a generator, I have not personally seen any motorhome that has microwave wired to inverter. I believe RV manufacturers fear owners will end up losing track of how much power they are using and kill the house batteries or overload inverter.
Powering microwaves from batteries is usually limited to do-it-yourself installations, modifications, and or upgrades where owner understands limitations. It is doable with proper installation.
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