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recommended power inverter

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Your limitation will be the 12V port. Ownership said it could handle up to 15A/180W but fortunately also included the relevant manual page, which clearly sez the 15A/180W is peak only. Iirc, 11A and 160W were the continuous numbers. Anyway, it's in the manual.

Would recommend a 12V adapter for your laptop. Got one for a MacBook Pro via Amazon and it works great. Less loss, too.

So that leaves the air mattress pump. Check the specs for a 400W and 800W inverter. A 400W will probably work fine.
 
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Ditto on buying 12V adapters. Inverters use a LOT more power, can overload 12V circuits, and generate more heat.

We have 12V adapters for our MacBook and MacBook Pro laptops and even a 32" Jensen LED HDTV in our RV that uses 12V power instead of using an inverter. Power consumption is king in our RV with just 232Ah of "house" battery... which is why we added a 327W SunPower E20 solar panel to it.