Transcript 1-3
1-3 1-3 Exponents Exponents Warm Up Problem of the Day Lesson Presentation Course Course 11 1-3 Exponents Warm Up Multiply. 1. 3 3 3 27 2. 4 4 4 64 3. 2 2 2 2 16 4. 5 5 5 5 625 Course 1 1-3 Exponents Problem of the Day Replace the letters a, b, and c with the numbers 3, 4, and 5 to make a true statement. 2a + 2a = bc 25+ 25 = 43 Course 1 1-3 Exponents Learn to represent numbers by using exponents. Course 1 1-3 Exponents Vocabulary exponent base exponential form Course 1 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 Course 1 3 = 7 7 7= 343 7 1-3 Exponents Course 1 Exponential Form 101 Read Multiply “10 to the 1st power” Value 10 10 1-3 Exponents Exponential Form Multiply “10 squared” or “10 to the 2nd power” 10 10 Value 100 Read Course 1 102 1-3 Exponents Exponential Form Multiply “10 cubed” or “10 to the 3rd power” 10 10 10 Value 1,000 Read Course 1 103 1-3 Exponents Course 1 Exponential Form 104 Read Multiply “10 to the 4th power” 10 10 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 5 5 54 5 is a factor 4 times. B. 3 3 3 3 3 35 Course 1 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 6 6 6 66 Course 1 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 2 2 2 = 64 B. 45 45 = 4 4 4 4 4 = 1,024 Course 1 1-3 Exponents Check It Out: Example 2 Find each value. A. 34 34 = 3 3 3 3 = 81 B. 25 25 = 2 2 2 2 2 = 32 Course 1 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 4th round. List the important information: • The secretary calls 4 families. • Each family calls 4 families. Course 1 1-3 Exponents 2 Make a Plan You can draw a diagram to see how many calls are in each round. Secretary 1st round – 4 calls 2nd round–16 calls Course 1 1-3 Exponents 3 Solve Notice that in each round, the number of calls is a power of 4. 1st round: 4 calls = 4 = 41 2nd round: 16 calls = 4 4 = 42 So during the 4th round, there will be 44 calls. 44 = 4 4 4 4 = 256 During the 4th round of calls, 256 families will have been notified. 4 Course 1 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 4th round. List the important information: • The secretary calls 3 families. • Each family calls 3 families. Course 1 1-3 Exponents 2 Make a Plan You can draw a diagram to see how many calls are in each round. Secretary 1st round – 3 calls 2nd round–9 calls Course 1 1-3 Exponents 3 Solve Notice that in each round, the number of calls is a power of 3. 1st round: 3 calls = 3 = 31 2nd round: 9 calls = 3 x 3 = 32 So during the 4th round, there will be 34 calls. 34 = 3 3 3 3 = 81 During the 4th round of calls, 81 families will have been notified. 4 Course 1 Look Back Drawing a diagram helps you see how to use exponents to solve the problem. 1-3 Exponents Lesson Quiz Write each expression in exponential form. 1. 12 12 12 123 2. 9 9 9 9 9 9 9 97 Find each value. 3. 202 400 4. 64 1,296 5. 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? 243 Course 1