How do the sixteenth, nineteenth, and twenty-sixth amendments change the relationship between state governments and the federal government?

Though there are rules that the state government can impose, the federal government can impose its power over the state that it can overrule the laws that the state government has, as long as, the federal government work within the powers stated in the Constitution.

Sixteenth Amendment:
"The Congress shall have power to lay and collect taxes on incomes, from whatever source derived, without apportionment among the several States, and without regard to any census or enumeration."

Nineteenth Amendment:
"The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of sex. Congress shall have power to enforce this article by appropriate legislation."

Twenty-sixth Amendment:
"The right of citizens of the United States, who are eighteen years of age or older, to vote shall not be denied or abridged by the United States or by any State on account of age. The Congress shall have the power to enforce this article by appropriate legislation"

Each of these amendments establishes new laws that apply to the entire nation. Before each of these amendments were passed, states could make their own choices about establishing voting ages, extending the right to vote, and collecting personal income taxes. Because the supremacy clause states that the Constitution is the supreme law of the land, all states have to follow these amendments. State laws cannot contradict these federal laws.