Is there a rule for the correct pronunciation of words starting with "ex"?

Solution 1:

First of all, this is British English, as the phonetic transcription [ɪk'stɜːmɪneɪt] makes clear ['kli:ə]. And this is a dialectal matter, so you should expect a lot of local and social variation on pronunciation, depending on what variety of English you speak.

The phonetics of the situation are very simple. English is a stress-timed language (as opposed to Romance languages, for instance, which are syllable-timed), which means that the natural unit of our speech is the stressed syllable, and the average time between stressed syllables is a constant in everyone's speech. We vary that rate for emphasis, but mostly it speeds up or slows down like music, rhythmically.

And in a stress-timed language with an unpredictable stress system, like English, there might well be two stressed syllables together with nothing between them (deFEND RUSSia), or there might be 3 or 4 unstressed syllables (dePENDing on whether the RUSSians do it) squeezed into that time. And when words get squeezed, I's get undotted and T's get uncrossed.

This is called Fast Speech Rules; it's a very popular part of phonological theory. And one of its important features in English is Unstressed Vowel Reduction. What this means is that, while American English has about a dozen phonemically distinct vowels (15 if you count diphthongs) in a stressed syllable, in an unstressed syllable very few can occur: predominantly /ə/ (with [ɨ] as a frequent allophone), but also /ɪ/.

Of the words cited by the original questioner, all but two follow the simple rule that unstressed /ɛ/ becomes /ɪ/. One is simply marked wrong -- exhale is stressed on the first syllable by most people; the contrast with inhale has overcome the tendency of bisyllabic verbs to be stressed on the second syllable.

And the other one -- extant -- has a primary stress on the second syllable, but there is also a secondary stress on the first syllable. English has at least three stress levels, and secondary stress (marked with a ˌ low apostrophe in the first syllable of words like rotational /ˌro'teʃənəl/) is common in long words. The dictionary these were taken from may not have marked secondary stress (many don't), or it may have been misplaced in transcription, but a native speaker would automatically give any unreduced initial /ɛ/ a secondary stress, so it's there whether it's marked or not.

Solution 2:

In English, vowels are often reduced in unstressed syllables, in this case meaning that [e] tends to become [ɪ]. This is what is going on here.

If the first syllable is stressed, it's eks. If the second syllable is stressed, it may be iks. I don't pronounce the first syllable of extant and expanse differently (both iks). So the only exception for me appears to be exhale, which I pronounce with more secondary stress on the first syllable than any of the iks words.

Look at the word extract. The stress changes depending on whether it is a noun or a verb, and so does the pronunciation of the first syllable.

And looking at the Merriam-Webster dictionary, some people pronounce extant with the accent on the first syllable; this is probably related to its being an exception.

Solution 3:

In my version of English, "exact" and "exhale" have the same vowel at the start of the word. But the phenomenon you describe isn't limited to "ex-", people pronounce "en-" in different ways too. I have a friend who says "injin" for "engine", and some people say "onvelope" for "envelope". In short: I think you can pronounce them "eks" all the time and it's probably not wrong.

Solution 4:

I believe the phonological rule may work like this:

• If the syllable ex- is stressed, the vowel is pronounced /ɛ/ (as in best); otherwise it can be (but is not necessarily) reduced to /ɪ/ (as the i in ignore). I think this applies to other first syllables with e/i sounds too. Whether or not the /ɛ/ is reduced probably depends on the speaker, dialect, etc.
• If the syllable ex- is stressed or if what follows is a voiceless consonant, it is pronounced /-ks-/; otherwise, it is /-gz-/. A voiceless consonant is one that does not involve vibration of the larynx, where the the vocal cords are; this includes f, s, sh, voiceless th (voiceless fricatives; the voiceless th is found in thick), and k, p, t (voiceless stops/occlusives).