How does a rocket propel its fuel in a space, where no air exists? Newton's Third Law cannot apply to this because, in Earth, rockets can push the air to propel, but in space, there is nothing to push.
This is not a question for this stack. It's purely a physics question. It may get closed for that reason, but I don't want you to leave here empty-handed, so I am going to stick a reply to it anyway.
This is actually one of the oldest misconceptions about rockets, the belief that they are "pushing against air". In reality, that is not what happens.
Sit in a boat, on a lake. Have someone load a bunch of boulders onto the boat - not too many, so you don't sink. Paddle away to the middle of the lake. Stop the boat. Now start throwing boulders overboard, vigorously pushing them one by one in the same direction. What happens then? The boat will start moving, in the direction opposite to the boulders.
Same effect could be achieved by throwing anything overboard, either something heavy like boulders, or something you could throw very fast, like bullets. There are videos on Youtube showing how you could "paddle" a boat by just shooting a gun in the same direction repeatedly - the boat will start moving in the opposite direction.
This is how rockets work. They are pushing, alright, you got that part straight. But they are not pushing against air - or against anything around them. They are pushing against the fuel. By throwing the fuel out at high velocity (like boulders or bullets from a boat), the rocket gets a kick in the opposite direction. That's what Newtons's third law says.
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.
"One body" here is the rocket. The "second body" here is the fuel; it's not the air. Fuel is also a body. Really, any body would do, just throw it fast enough. It doesn't have to be rocket fuel. It could be fluffy bunnies for all we care.
The rocket exerts a force on the burning fuel by throwing it out via the nozzle. Have you noticed how fast the fuel comes out of there? Yeah, there's a lot of force pushing it out of the nozzle, otherwise it would not come out like that. But then what does Newton's 3rd law say? Since the rocket is exerting force on the fuel, then the fuel, like for like, exerts force on the rocket.
That's how the rocket gets pushed up. It pushes the fuel really hard, down. So the fuel pushes the rocket up. One body pushes the other, and viceversa. No air needed at all.
Hope that helps. Physics is fun!