How can I write an essay supporting the idea that twenty-first century audiences can still relate to the nature of power and ambition highlighted in Macbeth?

In order to best write an essay supporting the idea that 21st century audiences can still relate to Macbeth, you truly need to understand the what Shakespeare wanted his audience to takeaway regarding the nature of power and ambition. First, ambition unchecked can lead people to commit evil acts. This means that if people are so ambitious they may be willing to break the law, commit a crime, or wrong someone. We often see acts like this everyday. For example, a students might cheat on a test in order to receive good grade.
Continually, Shakespeare wanted to highlight that power could cause people to act as a strong leader or an evil leader. The influence of power can seriously corrupt someone. There are many examples in modern times of leaders stealing money from their company or making decisions that are only best suited for the person in charge.
Thus, it would be a good idea to search NY Times or Wall Street Journal in order to find modern examples of power corruption or ambition unchecked.

You should start your essay with a strong thesis statement in which you express your sentiment on the topic. It is also essential that the statement makes clear what the focus of your essay will be and which direction it will take. I cannot provide an exact statement since you have to decide what you wish to focus on. I have provided a list of questions you should ask yourself once you have written a first draft of your thesis statement. This will definitely help you to formulate a powerful introduction. 
Is my statement specific?
Your statement should be focused. Your writing will be guided and will give the reader a clear idea about the subject of your essay.
Is my thesis statement too general?
The length of your essay determines this answer. Your thesis statement should have enough scope to cover all of the elements you wish to present in your essay.
Is my thesis statement clear?
You have to state exactly what direction your essay will take and make your position clear. Such clarity will provide the essay focus and inform the reader what, exactly, your essay is about.
Is my thesis statement original?
Try not to use others' words or cliched statements. It is important that the reader knows the ideas expressed are your own.
Once you are satisfied with your responses to these questions, you may create a final draft of your statement. A well-written thesis statement would indicate that you have considered it intelligently and that you are committed to what you write and are enthusiastic about it. 
The focus of your essay will obviously be the fact that modern audiences are, or have been, exposed enough to the themes of power and ambition illustrated in the play to understand them and, therefore, relate to them. Your essay should consider relevant examples from recent history that would highlight the desire for power, the achievement thereof, and possibly its outcomes.
Numerous examples exist. One can easily refer to events such as those in different conflict areas around the globe. In most of these situations, the fight for leadership and the manner in which it has been obtained and maintained, have been contentious. Once you have chosen a specific example or examples, it is essential that you relate these to the purpose of your essay.
Should you, for example, choose a specific leader or country, you have to indicate in what manner such an individual's rise to power has been reflected in his or her ambition. Which events preceded such a person's claim to or desire for power? How was such power eventually achieved? Your essay could provide a short narrative that offers the answer to each question.
Ensure that each example you use relates to the main theme of your essay. Since our two main characters, Macbeth and his lady, were corrupted by their ambition and their achievement, your essay should pertinently illustrate how the individuals on whom you focus have taken a similar route.
Furthermore, it is important that your essay is well structured. You should ensure a logical flow that makes it clear that you are heading toward a specific conclusion that, in this instance, would prove that modern audiences can still understand Shakespeare's notions of ambition and power as he displays it through the actions of his characters.
You can, in your conclusion, rephrase some of the points you made in your thesis statement or introduction. This will tie your paper together nicely. Make sure that the conclusion essentially reiterates the points you have made in a summary style.