If I were you, I would want to start off by looking at the famous scene where Lady Macbeth harangues her husband into sticking to his intention of killing Duncan in Act I scene 7. This is a very interesting scene to analyse, as she uses a number of different techniques to persuade her husband to do what she wants him to do, and in particular we can see how power and cruelty intersect through her power over her husband and some of the methods that she uses to manipulate him.
It is clear that at the beginning of the play at least, Lady Macbeth has power over her husband. She is cruel in the way that she intentionally mocks and shames her husband by arguing that it is cowardice that prevents him from putting his words into actions:
Art thou afeard
To be the same in thine own act and valour,
As thou art in desire? Would'st thou have that
Which tou esteem'st the ornament of life,
And life a coward in thine own esteem,
Letting "I dare not" wait upon "I would,"
Like the poor cat i'th'adage?
Note how she questions her husband's "manhood" in this passage, cruelly goading him on to doing the act that he does not wish to do. She continues by creating an incredibly cruel image of her dashing the brains of her baby out against a wall rather than break her promise. Thus we can see that there are definite examples of cruelty in her relationship with her husband and how she maintains her power over him.