Order of Operations - Special Cases

Special Cases

An exclamation mark indicates that one should compute the factorial of the term immediately to its left, before computing any of the lower-precedence operations, unless grouping symbols dictate otherwise. But 23! means (23)! = 8! = 40320 while 23! = 26 = 64; a factorial in an exponent applies to the exponent, while a factorial not in the exponent applies to the entire power.

If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:

Sometimes a heavy dot is used as a multiplication sign which indicates that the entire expression before the heavy dot is multiplied by the entire expression after the heavy dot, but this notation may be misunderstood. Thus x + y • a + b may be used for (x + y)(a + b), but the latter notation is more common.