Parallel passages: Mark 6:7; Luke 9:1. The prayer (Matthew 9:38) is answered in the persons of those who were taught to pray. Christ establishes his new agency. And when he had called unto him. From the circle of the bystanders.
His twelve disciples. Who had already been chosen to be specially with him (cf. Matthew 9:35, note; and Matthew 5:1). Twelve. To be heads of the tribes of the new Israel (Revelation 21:14; cf. James 1:1; Matthew 19:28).
Observe that the office of the tribes of the covenant nation corresponded to the symbolism of the number 12 (3, Deity, x 4, world = Church). He gave them power; authority (Revised Version); ἐξουσίαν: the greater including the less.
So Mark, but Luke expands to δύναμιν καὶ ἐξουσίαν. Against; over (Revised Version); simple genitive. Unclean spirits (Matthew 4:24. note). Unclean. As belonging to the unholy, non-theocratic kingdom, the realm of darkness.
"Hence also unclean animals (Matthew 8:31, sqq.; Revelation 18:2) and places (Matthew 12:43, sqq.) have a kind of natural relationship with such spirits" (Kubel). To cast them out. Their authority was to ex-send to this.
And to heal. Probably connected, not with ὥστε, but with ἐξουσίαν (cf. Luke). Observe that nothing is said of their receiving authority to convert. This God himself keeps. But they can remove all hindrances other than those purely subjective and spiritual, whether the objective hindrances be intruding evil spirits affecting body and mind or only bodily diseases.
All manner, etc. (Matthew 9:35, note).