hyphenation of compound adjectives

Question

Proofreading a friend's work, I came across the following phrase:

[teachers and students] work collaboratively to change long held, potentially incorrect and deeply believed views

Now, while I'm sure that in suggesting hyphenation for "long-held" and "deeply-believed" I'd be correct, for a reason I can't quite put my finger on I don't think hyphenating "potentially incorrect" would be appropriate. Am I correct, and if so, what distinguishes this phrase from the others?

The Chicago Manual of Style has a free 10-page pdf that covers hyphenation. You can find it by googling cmos hyphenation guide. See also the Related Questions here at ELU. — Arm the good guys in America, Jul 27 '18 at 20:42
Duplicate of adverb-adjective compound premodifier – with or without hyphen?. — Edwin Ashworth, Jun 06 '20 at 15:57

score 4 · Accepted Answer · answered Jul 27 '18 at 20:45

From The Chicago Manual of Style (17th ed), 7.86:

Compounds formed by an adverb ending in ly plus an adjective or participle (such as largely irrelevant or smartly dressed) are not hyphenated either before or after a noun, since ambiguity is virtually impossible. (The ly ending with adverbs signals to the reader that the next word will be another modifier, not a noun.)

While this is not the only style guide there is, this particular piece of advice is quite common.

Therefore, neither potentially nor deeply would be hyphenated:

[Teachers and students] work collaboratively to change long-held, potentially incorrect and deeply believed views.

hyphenation of compound adjectives

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