Which operation should be performed first for calculations involving more than one arithmetic operation?

Operations are performed according to the Order of Operations. Sometimes the mnemonic PEMDAS or BIDMAS is used to remind you what the order is.

P/B - parentheses/brackets. The content of these is evaluated first.

E/I - exponents/indices. Exponentiation is done first, right to left: a^b^c = a^(b^c).

MD/DM - multiplication and division are done in order of appearance, left to right. Each has equal priority, neither is done before the other unless it appears in the expression first. a/bc = (a/b)c. ab/c = (ab)/c

AS - addition and subtraction are done in order of appearance, left to right. Each has equal priority.

When functions are involved (sin( ), log( ), sqrt( ), for example), their arguments are evaluated according to the order of operations, then the function is evaluated, then the remainder of the operations are performed. For example, sin(a)^2 = (sin(a))^2. Sometimes, this is written sin^2(a).

When functions are written without parentheses around their arguments, it must be assumed that the function only applies to the first entity following the function name. log ab+c/d = (log(a)*b)+(c/d), for example, or √3x = (√3)x.