Would be very expensive. I've got 4 different inverters for my different vehicles (set up as mobile offices), so have some experience with these.
You first need to understand the 'load' that will come thru the plug. There are also numerous areas of power losses. The wattage of a microwave, is typically listed as the power that it will deliver to the food inside. The power that it will consume will be more than that wattage. You should find that on device there should be a placard indicating it's power usage, and it will be something like 10.0 amps @ 120Volts. (I just looked up a small 800 watt microwave on the internet, and the detail specs indicate it consumes 1.17KW = 10 amps). Wattage consumed is Volts x Amps, so 1200 watts.
The output of the inverter, then needs to power at least 1200 watts, and recognize that there are spike loads as well to worry about. A nice size inverter is 400 watt (800watt peak), which will typically power a laptop and other small miscellaneous phone chargers, etc. You can now get these on sale at PepBoys for like 30 bucks after rebates. (Vector is one brand name). A 1500-2500 watt inverter should run in the ballpark of $150-250.
The real killer, is that remember wattage is volts x amps. Since the input to the inverter is only 12volts, if you assume the inverter has 100% efficiency and no loss (which it doesn't), then you'd need a minimum of 100 Amps of input current, and they can't be very long. 100 Amps, depending on your vehicle, is close the max of an alternator running at full rev output). You're looking at something like #4 AWG wiring, fusing, and switching that someone would have to install and mount.
So technically do-able? Maybe, if you really paid attention to all of the current and voltage specifics of all of the devices.
Realistically do-able? No.
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