What are the terms for the powers granted to the states governments and what are two examples of those powers?

Answer 1

First of all, you have it backwards. It is the States that have granted power to the Federal government. Example: everything that has not been specifically granted to the Federal Government. Following are the powers that the States granted to the Federal government, right out of the US Constitution:

[Sorry for the length of this answer, but I feel it is important to note.]

"The Congress shall have Power To lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts and provide for the common Defense and general Welfare of the United States; but all Duties, Imposts and Excises shall be uniform throughout the United States; To borrow on the credit of the United States; To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes; To establish a uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States; To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures; To provide for the Punishment of counterfeiting the Securities and current Coin of the United States; To establish Post Offices and Post Roads; To promote the Progress of Science and useful Arts . . .

To constitute Tribunals inferior to the supreme Court; To define and punish Piracies and Felonies committed on the high Seas, and Offenses against the Law of Nations; To declare War, grant Letters of Marque and Reprisal, and make Rules concerning Captures on Land and Water; To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two Years; To provide and maintain a Navy; To make Rules for the Government and Regulation of the land and naval Forces; To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions; To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress; To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings; And To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof. Several amendments explicitly grant Congress additional powers. For example, the Sixteenth Amendment grants the power to "lay and collect taxes on incomes, from whatever source derived."