1 3 Exponents Learn to represent numbers by

1 -3 Exponents Learn to represent numbers by using exponents.

1 -3 Exponents Vocabulary exponent base exponential form

1 -3 Exponents An exponent tells how many times a number called the base is used as a factor. A number is in exponential form when it is written with a base and an exponent. Exponent Base 3 = 7 7 7= 343 7

1 -3 Exponents Exponential Form 101 Read “ 10 to the 1 st power” Multiply 10 Value 10

1 -3 Exponents Exponential Form 102 Read “ 10 squared, ” or “ 10 to the 2 nd power” Multiply 10 Value 100

1 -3 Exponents Exponential Form 103 Read “ 10 cubed, ” or “ 10 to the 3 rd power” Multiply 10 10 Value 1, 000

1 -3 Exponents Exponential Form 104 Read “ 10 to the 4 th power” Multiply 10 10 Value 10, 000

1 -3 Exponents Additional Example 1: Writing Numbers in Exponential Form Write each expression in exponential form. A. 5 5 54 5 is a factor 4 times. B. 3 3 3 35 3 is a factor 5 times.

1 -3 Exponents Check It Out: Example 1 Write each expression in exponential form. A. 7 7 7 73 7 is a factor 3 times. B. 6 6 6 66 6 is a factor 6 times.

1 -3 Exponents Additional Example 2: Finding the Value of Numbers in Exponential Form Find each value. A. 26 26 = 2 2 2 = 64 B. 45 45 = 4 4 4 = 1, 024

1 -3 Exponents Check It Out: Example 2 Find each value. A. 34 34 = 3 3 = 81 B. 25 25 = 2 2 2 = 32

1 -3 Exponents Additional Example 3: Problem Solving Application 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 4 th round. List the important information: • The secretary calls 4 families. • Each family calls 4 families.

1 -3 Exponents 2 Make a Plan You can draw a diagram to see how many calls are in each round. Secretary 1 st round– 4 calls 2 nd round– 16 calls

1 -3 Exponents 3 Solve Notice that in each round, the number of calls is a power of 4. 1 st round: 4 calls = 41 2 nd round: 16 calls = 4 4 = 42 So during the 4 th round, there will be 44 calls. 44 = 4 4 = 256 During the 4 th round of calls, 256 families will be notified. 4 Look Back Drawing a diagram helps you see how to use exponents to solve the problem.

1 -3 Exponents Check It Out: 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 4 th round. List the important information: • The secretary calls 3 families. • Each family calls 3 families.

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

1 -3 Exponents 3 Solve Notice that in each round, the number of calls is a power of 3. 1 st round: 3 calls = 31 2 nd round: 9 calls = 3 3 = 32 So during the 4 th round, there will be 34 calls. 34 = 3 3 = 81 During the 4 th round of calls, 81 families will be notified. 4 Look Back Drawing a diagram helps you see how to use exponents to solve the problem.