What types of power is designated solely to state governments according to a clause in the 10th amendment to the u. S. Constitution?

The answer is: reserved powers

Explanation:

"The powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people."

States must take responsibility for areas like:

property, education, implementation of welfare and other benefits programs, a justice system, local governments.