A numerical expression combines numbers and operations. The order of operations determines which parts are evaluated first, so the same notation gives the same result. Grouping symbols take priority. Inside each group, apply the same rules to whatever remains.
Multiplication and division have equal priority
Evaluate the innermost groups first, then powers and roots. Multiplication and division come next at the same level, from left to right. Addition and subtraction follow at the same level, also from left to right. The layout of a fraction or radical can group several terms, so read the extent of the bar before calculating.
In the first line, divide 24 by 6 before multiplying by 2. The second line adds parentheses around the product and therefore changes the divisor. The results, 8 and 2, are different.
Work outward from the innermost parentheses
In the following example, start with 2 plus 2. Inside the square brackets, divide 20 by 4 before subtracting 4. The bracket becomes 1. The power of 10 is 100, so the final product is 100.
A minus sign can be outside the power
A negative sign directly before a power is usually applied after exponentiation. Parentheses make a negative number the base, so squaring it produces a positive result. The same distinction matters when substituting a negative number into an algebraic formula.
