1. This document provides examples and explanations for simplifying expressions using exponents. It discusses the laws for taking the power of a power and the power of a product. 2. For the power of a power, you multiply the exponents. For the power of a product, you find the power of each factor and multiply them. 3. Several multi-step examples are worked through applying these laws to simplify expressions with variables and integers. The document also provides explanations of how rewriting numbers with exponents can make calculations easier.

1. Course 3, Lesson 1-4
Simplify. Express using exponents.
1. 48 43 2. (–3x6yz2)(–2xy3)
3. 4.
5. The population of Bangkok was 55 in 1620.
By 1990, it increased 54 times. What was
Bangkok’s population as of 1990?

12
7
9
9
5 10
3 3
a b
a b

2. Course 3, Lesson 1-4
ANSWERS
1. 411
2. 6x7y4z2
3. 95
4. a2b7
5. 1,953,125

3. WHY is it helpful to write numbers in
different ways?
The Number System
Course 3, Lesson 1-4

4. Course 3, Lesson 1-4 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
• 8.EE.1
Know and apply the properties of integer exponents to generate
equivalent numerical expressions.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
7 Look for and make use of structure.

5. To find the
• power of a power,
• power of a product
Course 3, Lesson 1-4
The Number System

6. Course 3, Lesson 1-4
The Number System
Words To find the power of a power, multiply the exponents.
Numbers Algebra
Examples
 
3
2 2 • 3 65 = 5 or 5   •=
n
m m na a

7. 1
Need Another Example?
2
Step-by-Step Example
1. Simplify using the Laws of Exponents.
(84)3
(84)3 = 84 • 3
Simplify.= 812
Power of a Power

8. Answer
Need Another Example?
Simplify (52)8 .
516

9. 1
Need Another Example?
2
Step-by-Step Example
2. Simplify using the Laws of Exponents.
(k7)5
(k7)5 = k7 • 5
Simplify.= k35
Power of a Power

10. Answer
Need Another Example?
Simplify (a3)7 .
a21

11. Course 3, Lesson 1-4
The Number System
Words To find the power of a product, find the power of each
factor and multiply.
Numbers Algebra
Examples
     
33 32 2 66 = 6 or 216x x x   =
m
m mab a b

12. 1
Need Another Example?
2
Step-by-Step Example
3. Simplify using the Laws of Exponents.
(4p3)4
(4p3)4 = 44 • p3 • 4
Simplify.= 256p12
Power of a Power

13. Answer
Need Another Example?
Simplify (3c4)3.
27c12

14. 1
Need Another Example?
2
Step-by-Step Example
4. Simplify using the Laws of Exponents.
(–2m7n6)5
(–2m7n6)5 = (–2)5m7 • 5n6 • 5
Simplify.= –32m35n30
Power of a Product

15. Answer
Need Another Example?
Simplify (−4p5q)2.
16p10q2

16. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
5. A magazine offers a special service to its
subscribers. If they scan the square logo
shown on a smartphone, they can receive
special offers from the magazine. Find the
area of the logo.
A = s2
Replace s with 7a4b.A = (7a4b)2
Area of a square
Power of a ProductA = 72(a4)2(b1)2
Simplify.A = 49a8b2
The area of the logo is 49a8b2 square units.

17. Answer
Need Another Example?
Find the volume of a cube with side lengths
of 6mn7 . Express as a monomial.
216m3n21 cubic units

18. How did what you learned
today help you answer the
WHY is it helpful to write numbers in
different ways?
Course 3, Lesson 1-4
The Number System

19. How did what you learned
today help you answer the
WHY is it helpful to write numbers in
different ways?
Course 3, Lesson 1-4
The Number System
Sample answer:
• Being able to write large numbers in exponential form
makes calculations easier.

20. Write a paragraph
telling how yesterday’s
lesson on the Product of
Powers law helped you
with today’s lesson.
Ratios and Proportional RelationshipsThe Number System
Course 3, Lesson 1-4