1. Zero and negative exponent properties Lesson 5
exponents
Zero and negative exponent properties
Lesson 5

2. a m • a n = a m + n = a m – n a m a n Review
What do we do when we want to multiply terms with the same base?
What do we do when we want to divide terms with the same base?
a m • a n
= a m + n
= a m – n
a m
a n

3. 4 7 4 9 = 4 7−9 4 7 4 9 Practice The exponent is negative?!!!
= 4 7−9
=4 −2 Subtracted Exponents
The exponent is negative?!!!
Let’s come back to this problem in a few minutes...

4. Where do we Use negative exponents?
The diameter of a human hair is about 10 −3 inches.
10 −3 is the same as or or 1 1,000

5. Where do we use negative exponents?
Chameleons and geckos can climb smooth, vertical surfaces because of tiny hairs on their feet that are 10 −4 meters long.
10 −4 is the same as or ,000 or

6. Negative and zero exponents
So what would we do with the 4 −2 we got in our earlier problem?
Let’s find out…

7. Negative and zero exponents
So how should we correctly write 4 −2 using only positive exponents?
4 −2 = = 1 16

8. Negative Exponent Property
For any integer a, and any exponent n≠0, 𝑎 −𝑛 = 1 𝑎 𝑛 or 𝑎 −𝑛 = 𝑎 𝑛
Algebra
Numbers
𝑎 −𝑛 = 1 𝑎 𝑛 or 𝑎 −𝑛 = 𝑎 𝑛
Words
Negative Exponent Property
3 −8 = or −8 = 3 8

9. 5 2 ∙ 5 −5 = 5 2+(−5) Product of Powers Property
practice
5 2 ∙ 5 −5
5 2 ∙ 5 −5 = 5 2+(−5) Product of Powers Property
= 5 −3 Adding Powers
= Definition of Negative Exponent
= Simplifying

10. 4 𝑛 −11 4 𝑛 −11 =4∙ 𝑛 −11 Rewriting the Expression
Practice
4 𝑛 −11
4 𝑛 −11 =4∙ 𝑛 −11 Rewriting the Expression
= 4 1 ∙ 1 𝑛 Definition of Negative Exponents
= 4 𝑛 Multiplying

11. 1 49 1 16 1 −16 100 7 −2 −2 −4 − 2 −4 10 −5 ∙ 10 7 Come to the board!
7 − −2 −4 − 2 − −5 ∙ 10 7 1 3 2 4 −

12. Come to the board!
5 𝑥 4 𝑥 𝑎 −4 𝑎 𝑏 2 ∙ 𝑏 −2 6∙ 6 −3 1 3 2 4
5 𝑥 𝑎