Applying Order of Operations to Expressions with Only Addition and Subtraction
Applying Order of Operations to Mixed-Operator Expressions
The Basics of Evaluating Equations

Applying Order of Operations in Expressions with Exponents

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:

image0.jpg

First, evaluate the exponent:

image1.jpg

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

image2.jpg

So

image3.jpg
  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
How to Tell One Differential Equation from Another
Find the Square Root of a Number
Solving Differential Equations Using Laplace Transform Solutions
How to Multiply Numbers
How to Solve Equations with Parentheses
Advertisement

Inside Dummies.com