Why does the Book of Mormon seem aware of the huge cultural impact of Egypt on Israel in 600 BC?

The Book of Mormon contains a strong Egyptian influence, including names and the language used on the gold plates.

FAIR Latter-day Saints asks:

Joseph Smith may have known that Hebrew was the language of Lehi, but how did he know of the huge cultural impact of Egypt on Israel in 600 B.C.? Lehi’s descendants used “Reformed Egyptian” to write on the metal plates for brevity, and the 2 languages/cultures clearly influenced the Book of Mormon people.
– FAIR Latter-day Saints – Book of Mormon Names

How would Joseph Smith know to include such a strong Egyptian influence in the Book of Mormon?

Hugh Nibley points out even the high proportion of Egyptian names is correct:

[W]e [can now] test certain proper names in the Book of Mormon in the light of actual names from Lehi’s world, unknown in the time of Joseph Smith. Not only do the names agree, but the variations follow the correct rules, and the names are found in correct statistical proportions, the Egyptian and Hebrew types being of almost equal frequency, along with a sprinkling of Hittite, Arabic, and Greek names.
– Hugh W. Nibley, An Approach to the Book of Mormon, 3rd edition, (Vol. 6 of the Collected Works of Hugh Nibley), edited by John W. Welch, (Salt Lake City, Utah : Deseret Book Company ; Provo, Utah : Foundation for Ancient Research and Mormon Studies, 1988), Chapter 22

Where would Joseph Smith have learned this? What experience did he have of ancient Egypt and its impact on Israel?

See:

FAIR Latter-day Saints – Book of Mormon Names

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