Evaluate exponents from left to right before you begin evaluating Big Four operations (adding, subtracting, multiplying, and dividing). The trick here is to turn the expression into a Big Four expression and then use the other basic order of operations rules.
The Three Types of Big Four Expressions
| Expression | Example | Rule |
|---|---|---|
| Contains only addition and subtraction | 12 + 7 - 6 - 3 + 8 | Evaluate left to right. |
| Contains only multiplication and division | 18 ÷ 3 x 7 ÷ 14 | Evaluate left to right. |
| Mixed-operator expression: contains a combination of addition/subtraction and multiplication/division | 9 + 6 ÷ 3 | 1. Evaluate multiplication and division left to right. 2. Evaluate addition and subtraction left to right. |
For example, suppose you want to evaluate the following:
3 + 5² - 6
First, evaluate the exponent:
3 + 25 - 6
At this point, the expression contains only addition and subtraction, so you can evaluate it from left to right in two steps:
= 28 - 6
= 22
So
3 + 5² - 6 = 22