Math Lesson 1.4.4 - Expressions Containing Exponents

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Welcome to our Math lesson on Expressions Containing Exponents, this is the fourth lesson of our suite of math lessons covering the topic of Order of Operations and PEMDAS Rule, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Expressions Containing Exponents

Expressions containing exponents are those algebraic expressions in which at least one of the numbers is raised by a given power. In these expressions, powers are calculated first, as they have a higher order of priority than multiplications and divisions (and obviously of addition and subtractions). Let's consider an example in this regard.

Example 5

Calculate the value of the following expression

21 - 3 × 7 + 24 ÷ 23 + 5 × 32 =

Solution 5

As we explained above, the terms containing exponents are calculated first. Since the two powers are not consecutive, we can calculate them simultaneously. We have

21 - 3 × 7 + 24 ÷ 23 + 5 × 32
= 21 - 3 × 7 + 24 ÷ 8 + 5 × 9

Now, we continue with the rest as in the previous examples (multiplications and divisions first, then additions and subtractions). We have

21 - 3 × 7 + 24 ÷ 8 + 5 × 9
= 21 - 21 + 3 + 45
= 0 + 3 + 45
= 3 + 45
= 48

More Order of Operations and PEMDAS Rule Lessons and Learning Resources

Arithmetic Learning Material
Tutorial ID	Math Tutorial Title	Revision Notes	Revision Questions
1.4	Order of Operations and PEMDAS Rule
Lesson ID	Math Lesson Title	Lesson	Video Lesson
1.4.1	Order of Operation in Arithmetic Expressions Containing Only Addition and Subtraction
1.4.2	Order of Operation in Arithmetic Expressions Containing Only Multiplications and Division
1.4.3	Expressions Containing Additions, Subtractions, Multiplications and Divisions
1.4.4	Expressions Containing Exponents
1.4.5	Expressions Containing Brackets. PEMDAS Rule
1.4.6	Types of Parenthesis and Their Order of Priority
1.4.7	Working with Negative Numbers
1.4.8	Powers of Negative Numbers

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