Nikolas had an idea that he could use the compressed carbon dioxide in a fire extinguisher to propel him on his skateboard. which of newton’s laws would he have used to come up with this idea?

The Newton’s law Nikolas would use to come up with this idea is the Third law that states:

When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

So, in this case, let's name the first Body A which is the skateboard and the second body B which is the compressed carbon dioxide in a fire extinguisher. Then, as shown in the figure below, according to the Third law: