1. Exponents
25 = ?

2. Vocabulary
exponent – the number of times a number is multiplied by itself.
base – the number that is being multiplied.
exponent 83
base
This is read “8 to the 3rd power” or “8 cubed.”
It means 8 x 8 x 8.

3. Evaluating Exponents 25
= 2 x 2 x 2 x 2 x 2
= 32
= 6 x 6 x 6
= 216 63
1.34
= 1.3 x 1.3 x 1.3 x 1.3 =

4. Exponents with a base of 10
Any multiple of ten can be expressed as an exponent with a base of ten.
The base is 10. The number of zeroes gives us the exponent.
Example: 100 = 102
10,000 = 104
1,000,000 =
106

5. Writing in Expanded Form Using Powers of 10
First, write the problem in expanded form.
Then, change each term to a multiplication of the value and its place.
Change the place values to exponents with powers of 10.

6. Example
7, 946 7,
(7 x 1,000) + (9 x 100) + (4 x 10) + (6 x 1)
7 x x x

7. Simplify.
1. 2  2  2
2. 3  3  3  3
3. 5  5  5
4. 4  4  4
5. 6  6  6  6  6 8 81
125 64
7,776

8. m • m • m = m3 Powers and Exponents
A simple way to think of exponents and powers is as repeated multiplication
m • m • m = m3

9. Key Terms exponent base
factor: when two or more numbers are multiplied together, each number is called a factor
exponent: an exponent tells how many times a number (called a base) is used as a factor
power: a number that is expressed using a base and an exponent
exponent
base

10. Powers and Exponents

11. Evaluating Powers Find each value. A. 44 44 = 4  4  4  4
Use 4 as a factor 4 times.
= 256
B. 73
73 = 7  7  7
Use 7 as a factor 3 times.
= 343
C. 191
191 = 19
Use 19 as a factor 1 time.

12. 43 72 27 35 106 171 Evaluating exponents Use 4 as a factor 3 times
4  4  4 = 16 43 72 27 35
106
171
Use 7 as a factor 2 times
7  7 = 49
Use 2 as a factor 7 times
2  2  2  2  2  2  2 = 128
Use 3 as a factor 5 times
3  3  3  3  3 = 243
Use 10 as a factor 6 times
10  10  10  10  10  10 = 1,000,000
Use 17 as a factor 1 time
171 = 17

13. Exponents
To express a whole number as a power, write the number as the product of equal factors. Then write the product using the base and an exponent.
For example, 10,000 = 10  10  10  10 = 104.

14. Expressing Whole Numbers as Powers
Write each number using an exponent and the given base.
A. 625, base 5
625 = 5  5  5  5
5 is used as a factor 4 times.
= 54
B. 64, base 2
64 = 2  2  2  2  2  2
2 is used as a factor 6
times.
= 26

15. Write each number using an exponent and the given base
7  7  7 = 73
256, base 2
2 2 2 2 2 2 2 2 = 28
1,000,000,000 base 10
10 10 10 10 10 10 10 10 10 = 109

16. Application
On Monday, Erik tells 3 people a secret. The next day each of them tells 3 more people. If this pattern continues, how many people besides Erik will know the secret on Friday?
On Monday, 3 people know the secret.
On Tuesday, 3 times as many people know as those who knew on Monday.
On Wednesday, 3 times as many people know as those who knew on Tuesday.
On Thursday, 3 times as many people know as those who knew on Wednesday.

17. Application: Continued
On Friday, 3 times as many people know as those who knew on Thursday.
Each day the number of people is 3 times greater.
3  3  3  3  3 = =
On Friday 243 people besides Erik will know the secret. 35
243

18. Scientists and mathematicians use exponential notation
To describe very large and very small numbers.
The average distance between the earth and the sun is
1 AU (astronomical unit) or about 93 million miles.
We can write that number as
Ninety three million
93,000,000
93 x 106
What advantage is there in using exponential notation to write very large numbers?