1. 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?
Course 3, Lesson 1-5

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

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

4. Mathematical Practices
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.
Course 3, Lesson 1-5 Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

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

6. Zero and Negative Exponents
The Number System
Zero and Negative Exponents
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
Course 3, Lesson 1-5

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

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

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

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

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

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

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

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

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

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

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

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

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

20. Need Another Example?
Simplify c2
Answer

21. How did what you learned today help you answer the
The Number System
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

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

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