1. ZERO POWERS
LESSON 17

2. X0 is defined to be equal to 1
ZERO EXPONENT
X0 is defined to be equal to 1
X0 = 1, where x  0
Exponent Law #4
Any non zero base raised to the exponent zero equals 1

3. EXAMPLES
30 = 1
(42  43)0 = 1 37 32 ( )
= 1

4. 1 , ( x  0) That is x-n = xn NEGATIVE EXPONENTS
x-n is defined to be the reciprocal of xn 1 xn
, ( x  0)
That is x-n =
Exponent Law #5

5. WHY IS THIS TRUE? WATCH THIS PATTERN 103 = 1000 102 = 100 101 = 10
100 = 1
10-1 = 0.1 or
10-2 = 0.01 or
Zero Exponent – Exponent Law #4 1 10
Negative Exponent – Exponent Law #5 1
100

6. EXAMPLES: ( ) ZERO EXPONENTS (-5)0 = 1 - 30 = -1 (20)3 = (1)0=1
(-3)0 = 1 2 5 ( )
= 1
- (3)0 = - (1) = -1
(-610)0 = 1

7. EXAMPLES 1 3 1 43 3-1 4-3 NEGATIVE EXPONENTS=
Remember that a negative exponent does not mean a negative number but the reciprocal number.
4-3 = 1 43

8. EXAMPLE
Long Version
Short Version =
4-5
4-3 
4-5
4-3 = 43 45 = 1 42 = 1 45  43
Flip Reciprocal to make positive powers
Subtract powers and place where there are more. 1 45 43 =  = 1 42 43 45 = =
4-2

9. EXAMPLE
Long Version
Short Version = 33
3-5  33
3-5 =
3335 1 = 38 = 33 1  35
Flip Reciprocal to make positive powers
Add powers and place where there are more. 33 1 35 =  = 38 = 33 35 

10. EXAMPLE
Long Version
Short Version =
5-2 54 
5-2 54 = 1
(52)(54) = 1 56 = 1 52  54
Flip Reciprocal to make positive powers
Add powers and place where there are more. 1 52 54 =  = 1 56 = 1
5254

11. CLASSWORK
Zero and Negative Power Handout – Lesson 17