Lesson: Exponents/Law of Exponents (Multiplying with Like Bases)

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Lesson Objective

SWBAT evaluate exponential numbers. SWBAT solve problems involving exponents. SWBAT derive and apply the law for multiplying exponential numbers with like bases.

Lesson Plan


6NSO.C17 – Apply the Order of Operations for expressions involving addition, subtraction, multiplication, and division with grouping symbols

6NSO.C15 – Apply laws of exponents to multiply whole number powers with like bases


Key Points

SWBAT solve problems with exponents (including law)


SWBAT solve order of operations problems with exponents

·         Exponents are repeated multiplication

·         For the law of exponents  (of multiplying exponential numbers with like bases)– the base stays the same and add the exponents

·         If an exponent is inside of a parentheses, evaluate the exponent first then complete the rest of the expression in the parentheses.


Exit Ticket:

1.       Which of the following expressions is equivalent to 43?

A.      4 x 3

B.      4 x 4 x 4

C.      3 x 3 x 3 x 3

D.      4 + 4 + 4


2.       What is the value of the following expression?        4 x (3 + 5)2



3.       Which of the following expressions is equal to 53 x 54?

A.      57

B.      512

C.      257

D.      2512


Do Now:

1.       Solve 4 x 4 x 4

2.       Solve:  4(3 + 5)

3.       Solve: 8 + (4 x 5)


Intro/Direct Instruction:

·         Today we are going to learn about exponents. 

·         Walk students through note pages:

·         First we need to know the vocabulary for explaining exponential numbers – the bigger number is called the base and the smaller raised number is called the exponent.

·         The way that we evaluate exponents is we multiply the base the number of times the exponent tells us to

·         Explain the way to read the numbers - __ to the blank power

·         Highlight that if the exponent is 2 we often say “squared”, so for example 32 is read three squared

·         Highlight that if the exponent is 3 we often say “cubed”

·         Model example of drawing the number of lines the exponent says, putting multiplication symbols between the line and then putting the base number on each line. Then to fully evaluate, we multiply all the parts out.

·         Review a second example:  53 = __ x __ x __   = 5 x 5 x 5 = 125

Guided Practice

·         Students practice: 

o    64

o    45

Direct Instruction:

·         Explain to students that sometimes we will have to look at problems with more than one exponent. 

·         Show example:  32 x 34

·         Tell students that in this problem the bases in both numbers are the same, they are both 3.

·         Tell students that when the bases are the same like this – we can simplify the problem quickly because there is a law that helps us to do so.

·         So, when the bases are the same our answer is also going to have the same base.  Then we are going to look at the exponents for each number and we are going to add them together.  So for this problem our answer is going to be 3 and since 2 + 4 is 6, it’s going to be 36

·         Show why this law works by expanding the exponents and then condensing them (3 x 3) x (3 x 3 x 3 x 3) = 37

·         Model example:  43 x 45

Guided Practice:

·         Students practice:  27 x 24, 73 x 75

Direct Instruction:

·         Now we know what an exponent is and what it does. 

·         As you know, we have been learning about order of operations in class and now we need to think about what happens when we have an exponent in an order of operations problem.

·         Sometimes in an order of operations problem the exponent will be directly outside of the parentheses:  4 x (9 – 4)2

·         In this case, we use the order of operations just as we learned them, first we need to solve the expression in the parentheses (9-4). 

·         Then we need to take the answer and use the exponent – 52 = 25, then we complete the rest of the problem.

·         Sometimes, the exponent will be inside of the parentheses.  Even though we hear Ms. PEMDAS saying parentheses first and then exponents – the only way to complete the part in the parentheses is to do the exponent so we need to do that first and then finish whatever else is in the parentheses. 

·         Walk through the example:  (62 ÷ 12) + 5

·         Make sure to emphasize the way the work should look – and organizing the problem for each step

Guided Practice:

·         Students practice: (10 – 6)3

·         (72 – 15) + 14

Independent Practice:

·         Students will complete worksheet

·         Teacher and students will review answers


·         Review key points

·         Students complete exit ticket

Lesson Resources

CW Exponents Unit1   Classwork
HW Exponents Unit1   Homework
Notes 7 Exponents   Notes


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