vacuum connected to power inverter

The 12 V sockets in the car are rated for 10 A or 120 W, not to mention your inverter is also clearly unsuitable. You'll just blow the fuse.

 

Yup! The fuse will blow so fast, you'll think the 12V outlet was already dead. Or you might hear a little click or pop as it blows.

 

Your best bet is a 14 gauge extension cord. Not a cheaper 16 awg cord which could burn out your vacuum cleaner. Even then your household vacuum is maybe 1/4 the power of a coin operated car wash vacuum.

A 150 watt inverter has no chance with a 1600 watt load. You would need a specialized pure sine wave inverter 10 to 11 times bigger and even then it would have to be connected directly to the 12v battery. A 1650 watt inverter would draw a staggering 137 amps of 12v power and require cables as thick as your little finger.

If there is no ac power within extension cord distance (maybe 100 feet), then a battery powered vacuum from a tool manufacturer like Makita or Milwaukee would be the next best thing. The 18v lithium batteries made to run power tools can output enough to come close to direct corded power. The motors in modern portable equipment are usually brushless which allows more battery power to be converted to mechanical work. If you already have an 18v tool platform, find a vacuum that uses those batteries.

 

how would that possibly 'save a ton'?

 

The 150 watt inverter might protect the car's fuse by blowing first.