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I am aware of the convention of stating an abbreviation in brackets the first time it is used, e.g. "I did well in the Biology Admissions Test (BAT)".

However, I am having difficulties with when you are already writing inside a bracket, e.g. "(I did well in the Biology Admissions Test (BAT))". I am not sure if using a bracket inside a bracket is correct. Would something like "(I did well in the Biology Admissions Test, or BAT)" be more appropriate?

Any advice would be appreciated!

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    There is nothing wrong with nested parenthesis, within reason. Your use case is very well within reason. – pgblu Oct 31 '16 at 13:13
  • I don't see a problem here. Is there some sort of dis-allowance pulled over you? Nobody put strict rules on this one. – SovereignSun Oct 31 '16 at 13:18
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Depends on your style guide. APA uses brackets:

When the spelled-out version first appears in parentheses, put the abbreviation in brackets after it:

Example: The diagnosis (i.e., attention-deficit/hyperactivity disorder [ADHD]) was confirmed via behavioral observation.

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