What is the basis for women being required to pray?

There aren’t any explicit instances of women praying in the Torah, but in the Prophets (1 Samuel Ch.1) we find a detailed account of Hannah’s prayer for a child and her prayer of thanks; many of the laws of prayer are derived (in the Talmud: Berachos 31) from this account. Maimonides derives the commandment of prayer from Deut.11:13, “... and to serve Him with all your heart”—the service of the heart is prayer (Talmud Taanis 2a). Since this commandment is observed at non-fixed times, it applies to men and women equally (Mishnah Berachos 3:3). The daily prayers are a Rabbinical ordinance; many women pray daily even though the daily prayers are said at specific times.