Joseph Fielding Smith speaks to the Priesthood authority women are given to "certain things in the Church" such as temple ordinances.
Joseph Fielding Smith, “Relief Society—an Aid to the Priesthood,” Relief Society Magazine 46, no. 1 (January 1959): 4
A person may have authority given to him, or a sister to her, to do certain things in the Church that are binding and absolutely necessary for our salvation, such as the work that our sisters do in the House of the Lord. They have authority given unto them to do some great and wonderful things, sacred unto the Lord, and binding just as thoroughly as are the blessings that are given by the men who hold the Priest-hood. And you sisters who labor in the House of the Lord can lay your hands upon your sisters, and with divine authority, because the Lord recognizes positions which you oc-cupy. He honors you and blesses you in your labors in your various stakes, and you go forth with authority.
You can speak with authority, because the Lord has placed authority upon you.