Jesus continued - "For in the resurrection they neither marry nor are given in marriage, but are like angels of God in heaven." Jesus, as God's Son, could state this authoritatively and declare that the Sadducees' assumption was false; that is, the institution of marriage does not exist beyond this world. Thus, their "difficult scenario" is not difficult for Jesus to answer and it certainly does not prove that there is no resurrection! In the afterlife, the woman wouldn't be a wife to any of her seven former husbands because she wouldn't be a wife, period! Let it be noted that one reason why the institution of marriage will not exist in the afterlife is because there will be no need for replacement reproduction since no one will die anymore (cf. Luke 20:36).
"But concerning the resurrection of the dead, have you not read what was spoken to you by God" - Carefully note that the subject Jesus mentions here is "the resurrection of the dead."
"I am the God of Abraham, the God of Isaac, and the God of Jacob" - It is very important to understand that those three men had been dead for many years when God spoke this message to Moses in Exodus 3:6. Specifically, Abraham had been dead for approximately 330 years, Isaac for 225 years, and Jacob for 198 years. Yet Jehovah was still their God! He did not say to Moses in the past tense: "I was the God of Abraham..." Rather, He spoke in the present tense: "I am the God of Abraham..." This implies that the patriarchs were still alive (though not in a physical sense), because "God is not the God of the dead, but of the living." This was strong evidence against the Sadducees' belief that, at the point of death, man ceased to exist. If their idea was true, then God was essentially stating to Moses that He was the God of nothingness or the God of those who don't exist, when He said: "I am the God of Abraham..." The falsity of such a statement was apparent to all who heard Jesus speak.
It is interesting to point out that although the subject matter Jesus was addressing pertained to the resurrection, our Lord actually only proved that one has a spirit that lives on after physical death. However, this evidently was sufficient to devastate the Sadducees' argument for it crushed their fundamental belief that there was no existence beyond physical death. They did not attempt to debate Him further on this matter (cf. Matt. 22:34).
The astonishment of the multitude probably arose from the fact that Jesus was able to answer the question of the Sadducees from the Scriptures. This was something that had evidently not been done by the Pharisees successfully. Luke 20:39 also mentions some of the scribes complementing Jesus on His answer. Evidently these men were not so bitter toward Him that they couldn't express admiration at the ease with which He answered a difficult question--a question that they had not been able to answer with their own limited wisdom.