In To Kill A Mockingbird, what are at least three ways in which Boo Radley is powerless against his brother Nathan Radley?

No one knows for sure what type of mental disability Arthur (Boo) Radley suffers from, but it's enough to keep him from being able to work a job or live alone. It also seems like Boo doesn't talk, so he can't or doesn't speak for himself. Tack on the fact that he stabbed his father in the leg with scissors when he was 3 years old and it all adds up to either confining Boo to an asylum, jail, or his own house where family can take care of him. After having Boo locked up in the basement of the courthouse for a while, the town and Mr. Radley decided to keep him at home. Scouts description of how Boo was handled comes down to the following:

"Nobody knew what form of intimidation Mr. Radley employed to keep Boo out of sight, but Jem figured that Mr. Radley kept him chained to the bed most of the time. Atticus said no, it wasn't that sort of thing, that there were other ways of making people into ghosts" (11).

After Mr. and Mrs. Radley died, Boo's older brother Nathan came home to take care of him. Calpurnia had once commented that the meanest man alive was Mr. Radley. Later, Scout mentions that "the only difference between them [Mr. Radley and Nathan Radley] was their ages" (12). This suggests that Boo's treatment at home under Nathan's care--whatever it was--probably continued in the same way it had been when his "mean" father was alive. 

From neighborhood reports, though, it seems as if Boo is permitted to go outside at night as long as he doesn't disturb anyone. Scout also mentions that Mr. Radley wouldn't speak to her, but Nathan would. Sadly, Nathan Radley stops any communication between Boo and the children when they use the knothole in the tree as a mailbox. Boo, in a childlike state of mind himself, was probably trying to reach out to the children by placing gifts in the tree for them. In an effort to control the innocent situation, Nathan fills up the knothole with cement and cuts off any connection Boo could have had with the kids.

Ultimately, Boo's mental limitations make him powerless against his brother. Boo can't speak for himself and he can't control impulses to harm people like his father and Bob Ewell. These things hold Boo back from being able to get a job, provide for himself, and live an independent life. Nathan, on the other hand, can do those things, so he takes care of his brother where his parents left off.