1. Course 3, Lesson 1-5
Use the four-step plan to solve each problem.
1. The Academic Boosters expect 475 people at the annual awards
banquet. If each table seats 6 people, how many tables are needed?
2. Kelsey was making treat bags for her classmates. She has already
made dozen bags. If she wants to have a treat bag for each of the
29 students in her class, how many more should she make?
3. Mrs. Bowman spent $110 to rent a popcorn machine for the school
carnival and $75 to buy popcorn, oil, and other supplies. If she sold
263 bags of popcorn for $1.50 each, how much money did she
make after paying for the machine and the supplies?
1
1
2

2. Course 3, Lesson 1-5
ANSWERS
1. 80 tables
2. 11 more bags
3. $209.50

3. WHY is it helpful to write numbers in
different ways?
The Number System
Course 3, Lesson 1-5

4. Course 3, Lesson 1-5 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
• use negative exponents,
• multiply and divide powers
using negative exponents
Course 3, Lesson 1-5
The Number System

6. Course 3, Lesson 1-5
The Number System
Words Any nonzero number to the zero power is 1. Any nonzero
number to the negative n power is the multiplicative inverse
of its nth power.
Numbers Algebra
Examples 05 1
  3
or
-3 1 1 1 17
7 7 7 7
 0 1, 0x x
, - 0
1
n
n xx x

7. 1
Need Another Example?
Step-by-Step Example
1. Write the expression using a positive exponent.
6–3
6–3 = Definition of negative exponent.

8. Answer
Need Another Example?
Write 4−4 using a positive exponent.

9. 1
Need Another Example?
Step-by-Step Example
2. Write the expression using a positive exponent.
a–5
a–5 = Definition of negative exponent.

10. Answer
Need Another Example?
Write c−7 using a positive exponent.

11. 1
Need Another Example?
Step-by-Step Example
3. Write the fraction as an expression using a
negative exponent other than –1.
= 5–2 Definition of negative exponent.

12. Answer
Need Another Example?
Write as an expression using a negative
exponent.
f–5

13. 1
Need Another Example?
2
Step-by-Step Example
4. Write the fraction as an expression using a
negative exponent other than –1.
= 6–2
Definition of exponent
Definition of negative exponent

14. Answer
Need Another Example?
Write as an expression using a negative
exponent.
3−2

15. 1
Need Another Example?
2
3
4
Step-by-Step Example
5. One human hair is about 0.001 inch
in diameter. Write the decimal as a power of 10.
= 10–3
1,000 = 103
Definition of negative exponent
0.001 = Write the decimal as a fraction.
=
A human hair is 10–3 inch thick.

16. Answer
Need Another Example?
A grain of salt has a mass of about 0.0001
gram. Write the decimal as a power of 10.
10–4

17. 1
Need Another Example?
2
3
Step-by-Step Example
6. Simplify the expression.
53 • 5–5
= or
Simplify.
Write using positive exponents. Simplify.
53 • 5–5 = 53 + (–5) Product of Powers
= 5–2

18. Answer
Need Another Example?
Simplify 4−5 · 4−3.

19. 1
Need Another Example?
2
Step-by-Step Example
7. Simplify the expression.
Subtract the exponents.
= w–1 – (–4) Quotient of Powers
= w(–1) + 4 or w3

20. Answer
Need Another Example?
Simplify .
c2

21. How did what you learned
today help you answer the
WHY is it helpful to write numbers in
different ways?
Course 3, Lesson 1-5
The Number System

22. How did what you learned
today help you answer the
WHY is it helpful to write numbers in
different ways?
Course 3, Lesson 1-5
The Number System
Sample answers:
• You can use a negative exponent to write very small
numbers without using a fraction.
• You can easily multiply or divide very large and very
small numbers with the same bases.

23. Write the following expressions
using a positive exponent:
3t−5
Ratios and Proportional RelationshipsThe Number System
1
r-2
Course 3, Lesson 1-5