Final answer:
The last infallible ex cathedra pronouncement was made by Pope Pius XII in 1950 concerning the Assumption of Mary, and it's the only time such authority was exercised after it was defined in 1869.
Step-by-step explanation:
The most recent use of an infallible definition ex cathedra occurred in 1950. This is when Pope Pius XII defined the Assumption of Mary as an article of faith for the Roman Catholic Church. This doctrine states that Mary, the mother of Jesus, was assumed body and soul into heavenly glory at the end of her earthly life. This event is significant as it's the only instance of infallible papal authority being exercised since the doctrine was formally established by the First Vatican Council in 1869. The concept of papal infallibility itself suggests that the Pope, when speaking ex cathedra, or 'from the chair' of Saint Peter, on matters of faith and morals, is preserved from the possibility of error.