Is 'ex' of 'extinct' pronounced differently from that of 'exactly'?

Question

This question below is from my English book exercise:

Choose the word whose underlined part is pronounced differently from that of the other words

a. exactly
b. exist
c. exhaust
d. extinct

(Because I couldn't underline the part of each word in this post, I made it bold)

After trying reading aloud each word a few times, I couldn't notice any differences of the above 'ex' parts. Then I looked it up in Oxford Dictionary and it showed each word's phonetic transciption like this:

a. exactly /ɪɡˈzæktli/
b. exist /ɪɡˈzɪst/
c. exhaust /ɪɡˈzɔːst/
d. extinct /ɪkˈstɪŋkt/

If the /ɪɡ/ and /ɪk/ are at the end of the word, like 'big' or 'tick', I can see the differences and pronounce them easily. However, in the exercise, it seems to me that the /ɡ/ and /k/ of all the words are canceled or silent.

Could you advise me on whether I'm correct or not in this case?

Answer 1

A native English speaker pronounces extinct differently from egg stinked (yes I know, that should be egg stank). extinct is pronounced with an unvoiced /k/ sound, and egg stinked with a voiced /g/ sound.

As you remark, there would be hardly any difference in this context if voicing were the only distinction. But in most dialects of English, a syllable-final unvoiced consonant preceded by a vowel is pre-glottalized. In some dialects, notably Cockney, the consonant (especially /t/) can disappear entirely, and all that's left is the glottal stop: "Wha' a lo'" for "What a lot".

See the Wikipedia article on Glottalization for a discussion of this.