Applying Order of Operations in Expressions with Exponents - dummies

Applying Order of Operations in Expressions with Exponents

By Mark Zegarelli

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:


First, evaluate the exponent:


At this point, the expression contains only addition and subtraction, so you can evaluate it from left to right in two steps: