Verily, verily, I say unto you, He that believeth on me, the works that I do shall he do also; and greater works than these shall he do; because I go unto my Father.

And whatsoever ye shall ask in my name, that will I do, that the Father may be glorified in the Son.

If ye shall ask any thing in my name, I will do it. - John 14:12-14

"Therefore, as I said unto mine apostles I say unto you again, that every soul who believeth on your words, and is baptized by water for the remission of sins, shall receive the Holy Ghost.
And these signs shall follow them that believe--
In my name they shall do many wonderful works;
In my name they shall cast out devils;
In my name they shall heal the sick;
In my name they shall open the eyes of the blind, and unstop the ears of the deaf;
And the tongue of the dumb shall speak;
And if any man shall administer poison unto them it shall not hurt them;
And the poison of a serpent shall not have power to harm them.
But a commandment I give unto them, that they shall not boast themselves of these things, neither speak them before the world; for these things are given unto you for your profit and for salvation." - D&C 84:64-73

"No matter who believeth, these signs, such as healing the sick, casting our devils, etc., should follow all that believe, whether male or female. He asked the Society if they could not see by this sweeping promise, that wherein they are ordained, if it is the privilege of those set apart to administer in that authority, which is conferred on them; and if the sisters should have faith to heal the sick, let all hold their tongues, and let everything roll on." Teachings of the Prophet Joseph Smith, Section Four 1839-42, p.224