I have a 09 chevy impala. My license plate light stopped working

SOURCE: license's plate light stopped working even with new bulb.

It wouldn't be a fuse if that's the only light that's not working, I believe all of the parking lights are on the same fuse. It's most likely a bad ground or corrosion inside the socket where the bulb makes the electrical connection. So check the socket to make sure it has no corrosion, if it does, clean it up and apply some dielectric grease (available at any parts store) to prevent future corrosion, and check for a loose or broken ground wire.

SOURCE: License plate lights do not work.

The licence plate lights are in the same line as your tail light wiring assembly. I assume your tail lights are working or you would have got a ticket for that. The wire is either cut, broken or unhooked from the tail light wires (which usually are brown). If you can not find the problem, you can always run a new wire to the tail light wire from your licence plate wire. Then they should work.
Your other problem is that the license plate ground is rusty & not grounding, which would also not let them work, so you should probably check that first. Rick

SOURCE: license plate light replacement

The license plate lights are in the ledge above the license plate. 2 screws keep the lens cover in place. Remove the screws, and the cover comes off. Just pull the lamp out (wedge base) and replace.

SOURCE: taillights and license plate lights not working

there is a short somewhere.put a test light in place of the fuse.
the light will glow bright.when the short is removed,the light will go dim

SOURCE: license plate bulb needs replacing

Remove license plate. Unscrew the screws on the underside of the bumper. Slide the lights back toward the trunk and then down through the opening. Unscrew bulb and replace with a new one.

Reverse steps to reinstall the lights.