How does Robert Mugabe exemplify the ideas of The Prince by Machiavelli?
As was the case with Hugo Chavez (or with any ruler we see as bad), Mugabe exemplifies the idea that a ruler should care only about maintaining his own power. All ideas about ethics or about helping his people should be secondary to the goal of staying in power.
Mugabe's methods of staying in power often are in accord with what Machiavelli says. For example, Machiavelli says that a ruler must not do small harms to people but rather harm them so badly that they will not take revenge on him. An example of this might be in Mugabe's treatement of whites in Zimbabwe. He has been so harsh with them (confiscating land, threatening or actually carrying out violence) that they have mostly chosen to leave rather than to resist.
In addition, Mugabe seems to hold to the idea that it is important to have people believe in you but then to be able to force them to obey when they have stopped believing. At first, people believed in him because he had been a leader of black resistance to white rule. But then, as people stopped believing in him, he was quite willing to resort to force to prevent people from rising up against him. He was willing to be feared rather than loved, just as Machiavelli recommends.