You have a couple of options to fix a severed power cord. You could splice the wires together, but a safer and easier option is to replace the jack on the end.
Bring in a 3-pronged replacement outlet. They are around $2 without a ground, or $3 with a ground.
Loosen the screw to open up the plug, and inside you’ll find three screws (2 if there is no ground).
From the severed cord, you’ll connect the black wire to the brass screw, the white wire to the silver screw, and the green/bare wire (ground) to the green screw. If you don’t have a green wire to connect to the green screw, don’t worry about it.
Carefully use an Xacto knife to open up the sheathing from the wires, a couple of inches up the cord. Be careful not to cut too deep- you don’t want to cut the wires themselves.
Peel back the sheathing to expose the wires
Cut off any extra sheathing
Once you have your black and white (and green if you have one) wires exposed, strip the sheathing from them using wire strippers.
Twist the little wires all together (in both the black and white separately) to makes sure they have good contact
Then make a hook with each of them to hook onto the screws inside the plug.
Loosen the screws in the plug a bit
Hook the black wire onto the brass screw, with the hook on the left of the screw, so as you tighten it, the wires tighten along with it. Do the same for the white wire to the silver screw.
If you have a ground, do the same to the green screw.
Close up the plug
Tighten the screw on the outside
Give it a tug to make sure it’s attached
Congratulations, you fixed your power cord!
Watch the video here!