0
A. Zero
B. One
C. The temperature outside
D. I am in the wrong class
What is Multiplication?
2x3=?
What is Multiplication?
Repeated Addition is Multiplication
Repeated Multiplication
2x2x2=?
Repeated Multiplication
2x2x2=8
3
2
2
3
3
10
Repeated Multiplication
2x2x2=8
3
2 =8
2
3 =9
3
10 = 1000
Exponents can be thought of as repeated multiplication
4
2 is multiplying 4 Twos
1 and -1 to different Powers
2
1 =
8
1 =
1 and -1 to different Powers
2
1 =1
8
1 =1
1
-1
2
-1
1000000000
What is 1
Any Number to the Power Zero
1
2
2
2
3
2
4
2
Any Number to the Power Zero
1
2
2
2
3
2
4
2
0
0 is an exception and is considered “undefined”.
Extending the Series – Negative Powers
What Zero is to Addition 1 is to multiplication
2+0=2
10 + 0 = 2
2x1=2
10 x 1 = 10
A Number Line of Exponents?
Revisiting Negative Exponents
1
2 =2=1x2
4
2 =2x2x2x2=1x2x2x2x2
-4
-4
2 =1x2
-3
3
-3
(-2)
5
−2
8
Multiplying and Dividing Powers
1
2
2 x2 =
-3
5
4 x4 =
Multiplying and Dividing Powers
−3
12
−2
12
Power of Power
1
2
3
3
2
3
Different Bases
2
3
3
2
3 x2
2 x4
Putting it all together
−8
(3
3 -2
x7 )
Swapping numbers with variables
(𝑎
−8
3 -2
x𝑏 )
The Final Problem