What's the pronunciation of 不在乎 All the dictionaries I've checked say


  bu4 zai4 hu5


but should it actually be 


  bu2 zai4 hu5


I get different answers searching for 不对， some dictionaries say bu4dui4 others bu2dui4, but as far as this phrase goes they all say bu4 zai4 hu, so is this some sort of exception to the tone change rules of 不？
Dictionaries, in general, will not incorporate tone sandhi rules into their pronunciations (of which Mandarin has quite a few)
Wikipedia says the following:

Mandarin Chinese
Mandarin features several sandhi tone rules.
When there are two 3rd tones in a row, the first one becomes 2nd tone,
and the second one becomes a half-3rd tone. E.g. 你好 (nǐ + hǎo = ní
hǎo)1
The neutral tone is pronounced &quot;low&quot; when following the 1st, 2nd, and
4th tones, and pronounced &quot;high&quot; following the 3rd tone.[dubious ]
不 (bù) is 4th tone except when followed by another 4th tone, when it
becomes 2nd tone. E.g. 不對|不对 (bù + duì = bú duì)
一 (Yī) is 1st tone when it represents the ordinal &quot;first,&quot; Examples:
第一个 (dìyīgè). It changes when it represents the cardinal number &quot;1&quot;
following a pattern of 2nd tone when followed by a 4th tone, and 4th
tone when followed by any other tone. Examples: 一个 (yī + gè = yí gè),
一次 (yī + cì = yí cì), 一半 (yī + bàn = yí bàn), 一般 (yī + bān = yì bān),
一毛 (yī + máo = yì máo), 一会儿 (yī + huǐr = yì huǐr).

The rules you need to learn yourself dictionaries will not help you out on this one.
So to answer your question anytime you see 不+4th-tone it will actually be pronounced 2nd tone+4th-tone