1. Negative Exponents
and
Zero Exponents

2. Negative & Zero Exponents
Multiply Integers REVIEW
= +1
1 • 1
1 • -1
= -1
-1 • -1
= +1
-1 • -1 • -1
= -1
-1 • -1 • -1 • -1
= +1
-1 • -1 • -1 • -1 • -1
= -1
-1 • -1 • -1 • -1 • -1 • -1
= +1
Odd # of Negatives = Negative
Even # of Negatives = Positive

3. Negative & Zero Exponents
22 Means… 2 • 2 = 4
21 Means… 2 = 2
20 Means… 1
What does 2-1 Mean?

4. Negative & Zero Exponents
What does 2-1 Mean?
You cannot leave an exponent negative because there is no way to express it’s meaning.
You must make it positive!

5. Negative & Zero Exponents
You do NOT want to have negative exponents in your answer. You get rid of them by flipping the exponent over, like reciprocals.
If the negative exponent is on top, move it to the bottom.

6. Definition of Negative Exponent
Negative & Zero Exponents
Definition of Negative Exponent
For any integer n,
a-n is the reciprocal of an

7. Definition of Negative Exponent
Negative & Zero Exponents
Definition of Negative Exponent
For any integer n,
a-n is the reciprocal of an

8. Definition of Negative Exponent
Negative & Zero Exponents
Definition of Negative Exponent
For any integer n,
a-n is the reciprocal of an

9. Negative & Zero Exponents
A negative exponent is an inverse!
Flip the number over to make the exponent positive!
Simplify.

10. Negative & Zero Exponents=
Follow the Pattern! =
3 3
Notice that anything to the zero power is always one! = 3 = 1 = = =

11. Negative & Zero Exponents
Follow the Pattern! 1 10 10 -1 1 10
= 0.1 10 1 2
100 3 -2 1 10 1
100
= 0.01
1,000 10 2 4
10,000 -3 1 10 1
1000
= 0.001 10 5
100,000 3

12. Negative & Zero Exponents
Study the table and FOLLOW THE PATTERN!
Exponent, n –1 2–2 2– Power, 2n 1 2 1 4 1 8 32 16 8 4 2 1
What do you think 2–4 will be?
2–4 = = 1
What do you think 2–5 will be?
2–5 = = 1

13. Negative & Zero Exponents
Study the table and FOLLOW THE PATTERN!
Exponent, n –1 3–2 3– Power, 3n 1 3 1 9 1 27
243 81 27 9 3 1
What do you think 3–4 will be?
3–4 = = 1
What do you think 3–5 will be?
3–5 = = 1

14. Negative & Zero Exponents
Negative Exponent:

15. Negative & Zero Exponents
Simplify.

16. Negative & Zero Exponents
Simplify.

17. Negative & Zero Exponents
Simplify.

18. Negative & Zero Exponents
Identity Property
Why It Works 2 -2 3 3
x0 = 1 9 9 = 1
Any number to the zero power is ALWAYS ONE.

19. Take Out Your Study Guide!!!
Negative & Zero Exponents
That's all Folks!
That’s all folks
Take Out Your Study Guide!!!

20. Powers of Ten
# 4 1 10 10 -1 1 10
= 0.1 10 1 2
100 3 -2 1 10 1
100
= 0.01
1,000 10 2 4
10,000 -3 1 10 1
1000
= 0.001 10 5
100,000 3

21. Negative Exponents For any integer n, a-n is the reciprocal of an # 5
EXAMPLES:
A negative exponent is an inverse!

22. Ex: # 6 Zero Exponent Any number to the zero power is ALWAYS ONE.