EXPONENTS

WARM-UP Estimate the Following 1)2, = 2)31, 231 – 1,232 = Round the Following Numbers to the 1000’s place 3) 34,498 4) 134, ,000 34, ,000

Do you remember “learning your doubles” when you were in 1 st grade? = = = = And so on….

Do you remember “learning your doubles” when you were in 1 st grade? How about this? 2 x 2 = 3 x 3 = 4 x 4 = 5 x 5 = And so on….

3 x 3 x  2  2   5  5  x 3 27

TRY THESE! Multiply  3   2   2  2  2 x  5  5

SAME THING??? Multiply  3   2   2  2  2 x  5  5

Learn to represent numbers by using exponents.

Vocabulary exponent base exponential form Insert Lesson Title Here

A number is in exponential form when it is written with a base and an exponent Base Exponent = 7  7  7= 343 An exponent tells how many times a number called the base is used as a factor.

Exponential Form10 1 Read“10 to the 1st power” Multiply10 Value10

Exponential Form10 2 Read “10 squared” or “10 to the 2nd power” Multiply 10  10 Value100

Exponential Form10 3 Read “10 cubed” or “10 to the 3rd power” Multiply 10  10  10 Value1,000

Exponential Form10 4 Read“10 to the 4th power” Multiply 10  10  10  10 Value10,000

You Try This One! 2 5 = 2x2x2x2x2 32!

WARM-UP Write the value of 2 4: in standard form? 16 Write 5 4 in in expanded form? 5 x 5 x 5 x 5 Write 9 2 in standard form! Write the value of 3 2: in standard form? 6 ? 9 Because 2 x 2 x 2 x 2

E X P O N E NT S Write 4 3 in expanded form? 4 x 4 x 4 Write 4 3 in standard form? 64

NEVER Add the numbers!

E X P O N E NT S Write 2 4 in expanded form? 2 x 2 x 2 x 2 Write 2 4 in standard form? 16

NEVER Multiply the Exponent by the Base!

Insert Lesson Title Here Additional Example 1: Writing Numbers in Exponential Form Write each expression in exponential form. A. 5  5  5  5 B. 3  3  3  3  3 5 is a factor 4 times is a factor 5 times. 3535

Insert Lesson Title Here Try This: Example 1 Write each expression in exponential form. A. 7  7  7 B. 6  6  6  6  6  6 7 is a factor 3 times is a factor 6 times. 6

Insert Lesson Title Here Additional Example 2: Finding the Value of Numbers in Exponential Form Find each value. A. 2 6 B = 2  2  2  2  2  2 = 64 = 4  4  4  4  4 = 1,024

Insert Lesson Title Here Try This: Example 2 Find each value. A. 3 4 B = 3  3  3  3 = 81 = 2  2  2  2  2 = 32

A phone tree is used to contact families at Paul’s school. The secretary calls 4 families. Then each family calls 4 other families, and so on. How many families will be notified during the fourth round of calls? 1 Understand the Problem The answer will be the number of families called in the 4th round. List the important information: The secretary calls 4 families. Each family calls 4 families. Problem Solving Application

You can draw a diagram to see how many calls are in each round. 2 Make a Plan Secretary 1st round – 4 calls 2nd round–16 calls

Solve 3 Notice that in each round, the number of calls is a power of 4. 1st round: 4 calls = 4 = 4 1 2nd round: 16 calls = 4 x 4 = 4 2 So during the 4th round, there will be 4 4 calls. 4 4 = 4  4  4  4 = 256 During the 4th round of calls, 256 families will have been notified. Look Back4 Drawing a diagram helps you see how to use exponents to solve the problem.

Try This: Example 3 A phone tree is used to contact families at Paul’s school. The secretary calls 3 families. Then each family calls 3 other families, and so on. How many families will be notified during the fourth round of calls? 1 Understand the Problem The answer will be the number of families called in the 4th round. List the important information: The secretary calls 3 families. Each family calls 3 families.

You can draw a diagram to see how many calls are in each round. 2 Make a Plan Secretary 1st round – 3 calls 2nd round–9 calls

Solve 3 Notice that in each round, the number of calls is a power of 3. 1st round: 3 calls = 3 = 3 1 2nd round: 9 calls = 3 x 3 = 3 2 So during the 4th round, there will be 3 4 calls. 3 4 = 3  3  3  3 = 81 During the 4th round of calls, 81 families will have been notified. Look Back4 Drawing a diagram helps you see how to use exponents to solve the problem.

Lesson Quiz Write each expression in exponential form  12   9  9  9  9  9  9 Find each value In a phone tree, each of three people will call three people, and then each of those will call three more. If there are five levels of the tree, how many people will be called? Insert Lesson Title Here 400 1,

Try this! Write the value of 2 4: in expanded form? 16 Write 5 4 in in expanded form? 5 x 5 x 5 x 5 Write 9 2 in standard form! 1881