The Constitution determines which power are to be held by the states by including an amendment that says so, more specifically the 10th Amendment, which, in order to limit the government's scope and give power to the states, established that all power not delegated to the federal government by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people.
For example, because the Constitution says nothing about granting the power to the government to make policy to regulate wages and working hours, each state has the power to make a policy regarding the issue, as long as it does not violate the Constitution.