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Order of operations

When a calculation has several operations, we need to know which one to do first to get the same answer every time. The order is: parentheses, then powers, then multiplication and division, and finally addition and subtraction.

()\ \to\ a^n\ \to\ \times,\div\ \to\ +,-

the order the calculation is carried out in

-a^2 = -(a^2),\quad (-a)^2 = a^2

the power applies only to the number without parentheses

Symbols

$()$	computed first
$a^n$	power, computed before $\times$ and $\div$

Example

$10 - 2\cdot(3 - 5) = 10 - 2\cdot(-2) = 10 + 4 = 14$ .

Subtracting a negative number is the same as adding it.

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