1. Do Now:
Write each of the following expressions using exponents. Then use a calculator to find the value of the expression.
2•2•2•2•2
(-4)•(-4)•(-4)
(-5)•(-5)

2. Negative Exponents
and
Zero Exponents

3. Reflect
Talk to your partner:
What is a general rule for the value of any number raised to the zero power: a0 =

4. Negative & Zero Exponents
Simplify.

5. Negative Exponents
You do NOT want to have negative exponents in your answer. An expression is NOT simplified when there is a negative exponent.
Turn and Talk: Have partner 2 talk now.
What is a general rule for the value of any number to a negative power? a-x =

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. What if the negative exponent is in the denominator?

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

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
Negative Exponent:

13. Negative & Zero Exponents
Simplify.

14. 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.

15. 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

16. Exit Ticket
Journal: 6 + (4=3)0 Explain how you would simplify this expression using the order of operations.