1. Exponents

2. How can I write 2 + 2 + 2 + 2 using multiplication?
Prior Knowledge
Years ago you learned that multiplication is an easier way to show repeated addition.
Example:
How can I write using multiplication?
2 x 4

3. How can I write 2 x 2 x 2 x 2 using exponents?
Exponential Form
Writing numbers in exponential form is just an easier way to show repeated multiplication.
Example:
How can I write 2 x 2 x 2 x 2 using exponents?
2 x 2 x 2 x 2 =
How many twos are shown? 24 1 2 3 4

4. 32 means 3 is multiplied by itself 2 times
Vocabulary
baseexponent
An exponent tells how many times a number (called the base) is multiplied by itself.
exponent 3²
base
32 means 3 is multiplied by itself 2 times

5. 4 is multiplied by itself 3 times
So… 43
4 is multiplied by itself 3 times
43 = 4 x 4 x 4 = 64
43 ≠ 4 x 3

6. There are two specially-named powers:
Reading Exponents
46 is read “4 to the sixth power.”
51 is read “5 to the first power.”
38 is read “3 to the eighth power.”
And so on…
There are two specially-named powers:
32 is read “3 to the second power” or “3 squared.”
43 is read “4 to the third power” or “4 cubed.”

7. Write each in exponential form and find the value.
2 x 2 x 2 x 2
7 x 7
1 x 1 x 1 x 1
5 x 5 x 5 6
24 = 16
72 = 49
14 = 1
53 = 125

8. Write each as repeated multiplication and find the value.32 33
101 25
3 x 3 = 9
3 x 3 x 3 = 27 10
2 x 2 x 2 x 2 x 2 = 32

9. What about a number raised to the power of ZERO?
Example: What is 30 ?
Complete the table below. See if YOU and your partner can see the pattern to figure it out…. 34
3x3x3x3 = 81 33 32 31 30

10. What about a number raised to the power of ZERO?
Example: What is 30 ?
Did you find that dividing by 3 gives you the next value? 34
3x3x3x3= 81 33
3x3x3 =27 32
3x3 =9 31 3 30 1

11. What about a number raised to the power of ZERO?
FACT: All positive numbers raised to the power of zero are equal to 1.
20 = 1
40 = 1
1,000,0000 = 1