Here the printer’s manuscript reads “the words of the prophets”, while the 1830 edition reads “the word of the prophets”. The 1905 LDS edition replaced word with words since the plural seemed more natural. The RLDS text adopted the plural reading in the 1908 edition, probably because 𝓟 had the plural. Either reading is theoretically possible, although elsewhere in the text, there are 13 occurrences of “the words of the prophets” but none of “the word of the prophets”. In fact, two of the examples of “the words of the prophets” are close by, including another one earlier in this same verse:
Thus the original manuscript probably read words both times in 3 Nephi 1:16.
Oliver Cowdery sometimes mistakenly wrote words instead of word, but in every case where the evidence is unambiguous he caught his error:
On the other side of the argument, there is one case where the 1830 typesetter replaced words with word (thus providing support for 𝓟 as having the original reading in 3 Nephi 1:16):
It should be noted that there are several more mix-ups of word and words in this part of the text where both 𝓟 and the 1830 edition are firsthand copies of 𝓞:
In each of these cases, as here in 3 Nephi 1:16, there is sufficient evidence from transmission errors to support either the manuscript scribe or the 1830 typesetter as the source for the variation. This means that the critical text will essentially follow the reading that works best contextually—that is, the reading that is most consistent with usage elsewhere in the text.
Summary: Accept in 3 Nephi 1:16 the plural words, the reading in 𝓟 (“those who believed in the words of the prophets”); the 1830 typesetter, it would appear, accidentally replaced words with word; elsewhere the text has instances of only “the words of the prophets”.