Operation sequence
Mathematical operations must be performed in a fixed order, that is
- 1. exponentiation and taking roots
- 2. multiply and divide
- 3. Add and subtract
A calculator also works according to these rules.
Explanation
The rules have been laid down by mathematicians to avoid confusion. They have no special meaning, but are well choosen. And you have to stick to them if you want to join the rest of the world.
History
Nothing is said about the use of brackets, which play a special role.
Example 1
The rules force a particular syntax, such as in
and so it is not
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Sometimes it has advantages to use brackets, if only for readability, because at
all is clear.
Example 2
In the calculation of
you must first perform the exponentiation, and only then take the square root. Thus
is completely wrong. The brackets must be solved from inside to outside, so