What simple machines are combined to make an axe?
An axe consists of a wedge at the end of a lever arm.
An axe uses a sharpened bit to chop through wood. From the top, it looks like this;
As the axe is swung at a chunk of wood, the wedge diverts energy to the sides, spreading the wood apart and making it easier for the cutting edge to cut through.
An axe needs a pretty good force to chop through something however, so the handle acts as a lever arm. The point of rotation, the axe wielder's shoulders, is the fulcrum of the lever. A longer handle can provide more torque to the axe head, which makes the chop more powerful.