Is it safe to power on a motherboard outside of its case?

Yes, it should be safe. Just be sure to put your motherboard on something not conductive, like cardboard box, and it should not touch anything that conducts electricity, including your main computer case. I did this few times. If you stop by in almost any computer shop, technicians do this sort of thing routinely.

Yes, you can power on the motherboard outside of its case. Just keep some precautions, like laying a piece of cardboard underneath the board, and you're good to go.

Also, human body contains static charge, so ground the static by touching a grounded appliance or wiring a ground circuit. Static charge in the human body might damage sensitive electronic components of the motherboard.

The other answers you got are correct: it's definitely doable and something that is done all the time by professional/power/enthusiast users for all sorts of purposes.

What I would like to add is that, if you search online, you'll see that a lot of people will turn the motherboard ON using a screwdriver: they simply close the circuit between the 2 power pins using the metal part of the screwdriver. This is done because you no longer have a power button (since there is no case). The electrical current in there is extremely small, so there's zero chance of harm.

However, be very very careful if you use this technique. Touching the wrong pins can damage the motherboard. They usually have some protections in there for situations where people don't connect the cables properly, but you shouldn't rely on this.

To mitigate these risks, there are 3 possible solutions:

• be super super careful when you do it
• get the power button out of your case and connect it normally. It should work. It's a simple circuit-breaker
• some motherboards (more expensive ones, dedicated to high-end PCs) have a power button on them. If yours does too, use that instead.

One thing to watch out for is add-in cards coming loose. On some cards, the rear connector bracket is long enough that it hangs below the bottom of the motherboard when the card is plugged in to the motherboard. This isn't a problem in a case when the motherboard is mounted on standoffs, but it can be a problem if you sit the motherboard directly on a hard flat surface - the weight of the motherboard can pull it away from the card, like so:

You may need to elevate the motherboard half an inch or so to prevent this.