The pronunciation is based on the sound of the letter, not the letter itself. If the sound is a vowel we use "an". If the sound is a consonant we use "a".
Sometimes "U" is pronounced the same as "you", as in "university". The initial sound is "y", which is a consonant. Any word that starts with "U" where it is pronounced with the "you" sound will use "a":
Articles precede nouns and adjectives, not verbs, in English. I think there have been other threads on this, but maybe only on words beginning with "h." In any case, "a" or "an" is always governed by whether the "u" has a "you" sound (an) or a "u" as in "un" sound (a).
By the way, James brought up the word ukulele, which is a nice example because most continental Americans pronounce it with you, hence a ukulele, but the Hawaiians I've heard speak, e.g. ukulele virtuoso Jake Shimabukuro, pronounce it as oo-koo-lay-lay (traditional pronunciation) and hence say an ukulele.
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Does anyone understand or know why my word document is wanting to change "an unilateral power" to "a unilateral power"? I realise that in spoken English we might just say a unilateral power because for me it seems easier to say it that way, but I would have thought in written English we would have abided by the whole a+consonant an+vowel.
I can give context behind it but I'm purely looking for the grammar explanation (if there is one, I realise English is strange!).
For what it's worth, either this rule was not always followed, or some words starting in U have changed in pronunciation over time. Thus, in the U.S. Constitution (1789), we see that Congress has the power to "establish an uniform Rule of Naturalization." I suppose it was pronounced ooniform at the time?