Final answer:
During A.D. 378 to 573, the Roman Empire faced invasions from barbarian groups like the Vandals, Goths, and Visigoths. The frozen Rhine River in 406 CE allowed the barbarians to bypass defenses and invade Roman territories. Rome was sacked multiple times, leading to the decline of Roman authority in the west.
Step-by-step explanation:
During the period from A.D. 378 to 573, the Roman Empire experienced several invasions from various barbarian groups. One major invasion occurred in 406 CE when a harsh winter froze the Rhine River, allowing barbarians to bypass the usual Roman defenses and invade Roman territories. The Vandals, originating from Germany, sacked their way into Spain and took control of a significant portion of the region. Additionally, the Goths and Visigoths, among other groups, sacked the city of Rome multiple times, resulting in the loss of Roman authority in the western part of the empire.