Translation
And when they saw the star they rejoiced exceedingly
Go to footnote numberwith great joy.
Go to footnote numberParaphrase
And when they saw how the star had guided them they rejoiced with the greatest intensity possible, and expressions of extreme joy.
Footnotes
1: “rejoiced exceedingly”
This word comes from a root which means “violently, or vehemently.” It expresses an extreme level of doing something, with 100% effort, we would say “all-out, to the max.”
2: "with great joy"
Here is another word that means the same thing; it is a double use of words that express intensity. Luke, under the inspiration of the Holy Spirit, was striving to communicate that very, very extreme emotion was expressed by these wise scholars. This method of showing emphasis is something I call “layering,” and the Greek language is very good at it because its grammar allows for one type of emphatic word or phrase to be piled on top of another, and another, etc.
They were overflowing with joy because this was the confirmation that all their study and all their effort to make the long journey were worthwhile. They were proven right. It took a great deal of faith in the prophecies to make this journey; now their faith was being rewarded.