The order of operations is a standard for how math expressions should be evaluated. This standard guarantees that two different mathematicians will compute the same result from an expression. The order of operations is listed below.

- Parentheses
- Exponents and Logarithms
- Multiplication and Division
- Addition and Subtraction

Shown below is a basic example where the order of operations is used to produce the same result.

This example contains two operations: addition and multiplication. Since multiplication appears before addition, the multiplication operation should be evaluated first.

Then, the addition operation is performed as well, leaving the result of the calculation.

**Note**, if the addition operation had been performed *before multiplication*, a different result would be caluclated instead.

Parentheses are used to disambiguate and even change the meaning of a math expression. For example, the expression below uses parentheses to *change* the order of operations and produce a different result.

To compute the result of this expression observe that the first thing to do is evaluate expressions contained within parentheses. In this case, that means evaluate the expression . This is shown below.

Finally, we are left with only the multiplication operation which we perform.

This gives us the result .