I am not sure that you really can say that all of the three branches of government are equally powerful. But if I had to argue that they were, I would say that it is because each can sort of cancel out an action of the other.
For example, the President can veto a law that Congress has passed. In turn, Congress can override the President's veto if it has enough votes.
When it comes to the judicial branch, they can say that a law passed by Congress or an action of the President in unconstitutional.
In that way, each branch can cancel out things the others do. This, you can argue, makes them all equal.