مَا كَانَ لِبَشَرٍ أَنْ يُؤْتِيَهُ اللَّهُ الْكِتَابَ وَالْحُكْمَ وَالنُّبُوَّةَ ثُمَّ يَقُولَ لِلنَّاسِ كُونُوا عِبَادًا لِي مِنْ دُونِ اللَّهِ وَلَٰكِنْ كُونُوا رَبَّانِيِّينَ بِمَا كُنْتُمْ تُعَلِّمُونَ الْكِتَابَ وَبِمَا كُنْتُمْ تَدْرُسُونَ | It does not behoove any human that Allah should give him the Book, judgement and prophethood, and then he should say to the people, ‘Be my servants instead of Allah.’ Rather [he would say], ‘Be a godly people, because of your teaching the Book and because of your studying it.’ | Aal-i-Imraan : 79
It's translated as godly people but Rabiniyeen has a meaning of being a religious scholar as well as pious as well as free of love of dunya. Worshiping God sincerely is part of it, but the word has other implications. You can look up the word: رَبَّانِيِّينَ and look up definition of it.
So women are to educate and learn, and you can search the lives of Fatima Al-Zahra (a) daughter of Mohammad (s), Zainab (a) sister of Hussain (a), and Al-Masooma (a) and what Imam Reda (a) said about her. Also Khadija (a) research her life before Nubuwa Mohammad (a) and after, since she is considered a holy exalted lady as well.
Not only women are to be educated they are to be politically active and participate in society.
As for the right to vote:
وَالَّذِينَ اسْتَجَابُوا لِرَبِّهِمْ وَأَقَامُوا الصَّلَاةَ وَأَمْرُهُمْ شُورَىٰ بَيْنَهُمْ وَمِمَّا رَزَقْنَاهُمْ يُنْفِقُونَ | those who answer their Lord, maintain the prayer, and [conduct] their affairs by counsel among themselves, and they spend out of what We have provided them; | Ash-Shura : 38