Which amendment to the constitution prevented states from denying men the right to vote on the basis of race?

Hi. It is the fifteenth amendment to the constitution that prevented states from denying men the right to vote on the basis of race.

I hope this help.

Take care,
Diana

The answer is the Fifteenth Amendment. 

This amendment granted African American men the right to vote and or anyone of a different race.

 Hope this helps!

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