The statement that best describes the expansion of Rousseau's idea of equality is that "Rousseau believed that education was the path to social equality for women."
The expansion of the idea of equality held by Enlightenment thinker Jean-Jacques Rousseau, as reflected in the Nineteenth Amendment to the US Constitution, is best described by the statement: "Rousseau believed that education was the path to social equality for women."
Rousseau's philosophy emphasized the importance of education in achieving social equality, and the granting of the right to vote to women through the Nineteenth Amendment can be seen as a step towards realizing this principle.
The amendment, ratified in 1920, prohibited the United States and its states from denying the right to vote to citizens of the United States on the basis of sex, effectively recognizing the right of women to vote.
This aligns with Rousseau's belief in the significance of education as a means to attain social equality for women. Therefore, the statement that best describes the expansion of Rousseau's idea of equality is that "Rousseau believed that education was the path to social equality for women."