Course Exponents 1-3 Exponents Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Course Exponents Warm Up Multiply  3   4   2  2   5  5  5

Course Exponents Problem of the Day Replace the letters a, b, and c with the numbers 3, 4, and 5 to make a true statement. 2 a + 2 a = b c = 4 3

Course Exponents Learn to represent numbers by using exponents.

Course Exponents Vocabulary exponent base exponential form

Course Exponents 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.

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

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

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

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

Course Exponents 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

Course Exponents Check It Out: 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

Course Exponents 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

Course Exponents Check It Out: Example 2 Find each value. A. 3 4 B = 3  3  3  3 = 81 = 2  2  2  2  2 = 32

Course Exponents 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. Additional Example 3: Problem Solving Application

Course Exponents 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

Course Exponents 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  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.

Course 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 4th round. List the important information: The secretary calls 3 families. Each family calls 3 families.

Course Exponents 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

Course Exponents 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.

Course Exponents 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? ,