CONFIDENTIAL 1

Warm-up: 1.) 2 x 2 x 2 =8

2.) 5 x 5 =25

3.) 4 x 4 x 4 =64

4.) 10 x 10 x 10 =1000

CONFIDENTIAL 2

Remember that any number can be written as a product of Prime Factors.

Example: 32

2 16

2 82

422 2

2 2 2 2 2

The Number 32 can be written as 2 x 2 x 2 x 2 x 2

CONFIDENTIAL 3

Example: 32

2 16

2 82

422 2

2 2 2 2 2

The Number 32 can be written as 2 x 2 x 2 x 2 x 2

A product of prime numbers can be expressed using EXPONENTS and a BASE

25

CONFIDENTIAL 4

Numbers expressed using Exponents are called Powers

Powers Words Expressions Value

25

32

103

2 to the fifth power

3 to the second power or 3 squared

10 to the third power or 10 cubed

2 x 2 x 2 x 2 x 2

3 x 3

10 x 10 x 10

32

9

1,000

CONFIDENTIAL 5

There are several symbols you might see for

Multiplication

2 x 2 x 2 = 23 2 * 2 * 2 = 2 3

2 2 2 = 23. .

CONFIDENTIAL 6

Let's Practice...

If we write 3 x 3 x 3 x 3 using an exponent,

the base is 3 AND

the exponent is 4

3 3 3 3 = 34 = 81 . . .

CONFIDENTIAL 7

We can also refer to writing 45 as a

PRODUCT OF THE SAME FACTOR

(Remember that a "Product" is the answer to a multiplication problem.)

The Base is 4. The Exponent is 5. So 4 is a Factor 5 times.

45 = 4 x 4 x 4 x 4 x 4 = 1,024

CONFIDENTIAL 8

Your Turn!

Write 7 x 7 x 7 using an Exponent. Then find its value.

73 = 343

CONFIDENTIAL 9

Write 23 as a product of the same factor. Then find its value.

2 x 2 x 2 = 8

CONFIDENTIAL 10

Exponents can be used to write the

Prime Factorizationof a number.Example

:24

2 12

2 62

32 2 2

x

x

x x

xx OR23 x 3

(Start with the smallest prime factor)

CONFIDENTIAL 11

Your Turn!

Write the Prime Factorization of the number using Exponents.

902 45

2 15

3

52 3 3

x

x

x x

xx OR2 x 32 x 5

CONFIDENTIAL 12

Your Turn!

Write the Prime Factorization of the number using Exponents.

1202 60

2 30

2

15

2 2 2

x

x

x x

xx OR23 x 3 x 5

2 2 2x xx 3 x 5

CONFIDENTIAL 13

Any number to the 1 power equals itself.

Example: 101 = 10

51 = 5

2,3451 = 2,345Any number to the 0 power equals 1.

Example: 100 = 1

50 = 1

2,3450 = 1

CONFIDENTIAL 14

Practice Problems:Write each product using an exponent. Then find its value.

1.) 2 x 2 x 2 x 2 = 24 = 16

2.) 6 x 6 x 6 = 63 = 216

Write each power as a product of the same factor. Then find its value.

3.) 26 = 2 x 2 x 2 x 2 x 2 x 2 = 64

4.) 34 = 3 x 3 x 3 x 3 = 81

Write the prime factorization of this number using exponents.

5.) 48 2 24

2 122

62 2 2

x

x

x x

xx

OR24 x 3

48

2 2 2x x 2 x 3x

CONFIDENTIAL 15

6.) Find the value of

51

7.) Find the value of

2360

= 5

= 1

CONFIDENTIAL 16

Write the values for these powers of 10.

a) 101 = 10

b) 102 = 100

c) 103 = 1,000

d) 104 = 10,000

e) 105 = 100,000

f) Describe the pattern for the powers of 10.

The next value is found by dividing the previous power by 10

CONFIDENTIAL 17

An estimated 109 people in the world speak MandarinChinese. About how many people speak this language? 109 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10

= 1,000,000,000

CONFIDENTIAL 18

1. Can you write this product using an exponent?

6 x 6 x 6 x 6 = 64

2. Can you find the value of this product?

5 x 5 x 5 = 53 = 125

3. Can you write this power as a product of the same factor?

36 = 3 x 3 x 3 x 3 x 3 x 34. Can you find the value of this power?

24 = 2 x 2 x 2 x2

Let's see how well we know Powers and Exponents!

CONFIDENTIAL 19

6. Find the prime factorization of this number using exponents.

20

5. Can you find the value of this power?

570 = 1

2 10

2 52

x

x x

OR 22 x 5

CONFIDENTIAL 20

Well Done!!

We learned that POWERS are numbers expressed using exponents. 34

We learned that a product of prime factors can be written using a Base and Exponents.

23 = 2 x 2 x 2 = 8

We learned how to find the value of 43

4 x 4 x 4 = 64

We learned how to write the Prime Factorization of a number using exponents.

24 = 2 x 2 x 2 x 3 = 23 x 3