This document provides a lesson on exponents. It includes examples of exponential expressions with whole number and fractional bases. Students are asked to evaluate expressions, write them in exponential, expanded, and standard form. The lesson defines exponential notation and explains that raising a number to the power of 0 equals 1, while whole number exponents get larger and fractional exponents get smaller as the exponent increases.

1. Lesson 5: Exponents
Date: 3/13/14 S.13
13
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 5
Lesson 5:Exponents
Classwork
Opening Exercise
As you evaluate these expressions, pay attention to how you arrived at your answers.
Examples 1–5
1.
2.
3. =
4. =
5. =
Go back to Examples 1 – 4 and use a calculator to evaluate the expressions.
What is the difference between and ?

2. Lesson 5: Exponents
Date: 3/13/14 S.14
14
©2013CommonCore,Inc. Some rights reserved.commoncore.org
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 5
Examples 6–8
6. =
7.
8.
The base number can also be a fraction. Convert the decimals to fractions in Examples 7 and 8 and evaluate. Leave your
answer as a fraction. Remember how to multiply fractions!
Examples 9–10
9.
10.

3. Lesson 5: Exponents
Date: 3/13/14 S.15
15
©2013CommonCore,Inc. Some rights reserved.commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 5
Exercises
Fill in the chart, supplying the missing expression.
1. Fill in the missing expression for each row. For whole number and decimal bases, use a calculator to find the
standard form of the number. For fraction bases, leave your answer as a fraction.
Exponential Form
Written as a Multiplication Expression
Having Repeated Factors
Standard Form
2. Write “five cubed” in all three forms (exponential form, written as a series of products, standard form)
3. Write “fourteen and seven tenths squared” in all three forms.
4. One student thought two to the third power was equal to six. What mistake do you think they made and how would
you help them fix their mistake?

4. Lesson 5: Exponents
Date: 3/13/14 S.16
16
©2013CommonCore,Inc. Some rights reserved.commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 5
Problem Set
1. Complete the table by filling in the blank cells. Use a calculator when needed.
Exponential Form Written as a Series of Products Standard Form
2. Why do whole numbers raised to an exponent get greater while fractions raised to an exponent get smaller?
3. The powers of that are in the range through are , , , , , , , , and . Find all the
powers of that are in the range through .
4. Find all the powers of in the range through .
5. Write an equivalent expression for using only addition.
6. Write an equivalent expression for using only multiplication.
a. Explain what is in this new expression.
b. Explain what is in this new expression.
7. What are the advantages to using exponential notation?
8. What is the difference between and ? Evaluate both of these expressions when .
Lesson Summary
Exponential Notation for Whole Number Exponents: Let be a non-zero whole number. For any number , the
expression is the product of factors of , i.e.,
The number is called the base, and is called the exponent or power of .
When is , “the product of one factor of ” just means , i.e., . Raising any non-zero number to the
power of is defined to be , i.e., for all .