What are the powers of the U.S. Supreme court?

They can decide if a law is constitutional or unconstitutional. For example, in Plessy v. Ferguson (1896), the Court decided segregation was constitutional. Then in Brown v. Board of Education (1954), the Court decided that "separate educational facilities are inherently unequal." Thus school segregation was suddenly unconstitutional. In Roe v. Wade, the Court decided that laws against abortion violated the constitutional right to privacy.