Yes
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Individual state may set any qualifications they choose for voting as long as those qualifications are not in conflict with the United States Constitution or Federal Laws. Most qualifications involve timeliness of registering.
It is true that many of the new state constitutions removed the property qualifications for voting. In 1790 in the United States, the only people who had the right to vote were white adult males who owned property.
power of state government
The people who are voting have a lawyer that does it
It was made this way because of the widespread variation of voting requirements in all the states.