Question

State governments have the power to

Answer 1

issue licenses (marriage,driving,etc.), regulate in state businesses, conduct elections, take measures for public health and safety, may use powers that are not given to the federal government and are not banned from the states, makes laws so long as they are constitutional 

Answer 2

Here's your complete answer-

State governments have the power to establish local governments, all other three are prerogatives of the federal government