To whom did Christ give the power to teach, to sanctify, and to rule the members of His Church? Christ gave the power to teach, to sanctify, and to rule the members of His Church to the apostles, the first bishops of the Church.
He who hears you, hears me; and he who rejects you rejects me; and he who rejects me, rejects him who sent me. (Luke 10:16)
Did Christ intend that this power should be exercised by the apostles alone? No, Christ intended that this power should be exercised also by their successors, the bishops of the Church.
And they prayed and said, "Thou, Lord, who knowest the hearts of all, show which of these two thou has chosen to take the place in this ministry and apostleship from which Judas fell away to go to his own place." (Acts 1:24-25)
Further reading: CCC 874-879