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EXPONENTS WARM-UP Estimate the Following 1) 2,129 + 998 = 3000 2) 31, 231 – 1,232 = 30,000 Round the Following Numbers to the 1000’s place 3) 34,498 4) 134,556 34,000 135,000 Do you remember “learning your doubles” when you were in 1st grade? 2+2= 3+3= And so on…. 4+4= 5+5= Do you remember “learning your doubles” when you were in 1st grade? How about this? 2x2= 3x3= And so on…. 4x4= 5x5= 9 9x3 3x3x3 3. 2 2 2 2 16 4. 5 5 5 5 625 27 TRY THESE! Multiply. 1. 3 3 3 2. 2 2 2 3. 2 2 2 2 x 2 4. 5 5 5 27 8 32 125 SAME THING??? Multiply. 1. 3 3 3 2. 2 2 2 3. 2 2 2 2 x 2 4. 5 5 5 27 8 32 125 Learn to represent numbers by using exponents. Insert Lesson Title Here Vocabulary exponent base exponential form 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 Exponential Form 101 Read Multiply “10 to the 1st power” Value 10 10 Exponential Form 102 Multiply “10 squared” or “10 to the 2nd power” 10 10 Value 100 Read Exponential Form 103 Multiply “10 cubed” or “10 to the 3rd power” 10 10 10 Value 1,000 Read Exponential Form 104 Read Multiply “10 to the 4th power” 10 10 10 10 Value 10,000 You Try This One! 5 2 = 2x2x2x2x2 32! WARM-UP Write the value of 24: in standard form? Because 2 x 2 x 2 x 2 Write 54 in in expanded form? 16 5x5x5x5 Write 92 in standard form! 18 Write the value of 32: 81 in standard form? 6? 9 E X P O N E NT S Write 43 in expanded form? 4x4x4 Write 43 in standard form? 64 NEVER Add the numbers! E X P O N E NT S Write 24 in expanded form? 2x2x2x2 Write 24 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 54 5 is a factor 4 times. B. 3 3 3 3 3 35 3 is a factor 5 times. Insert Lesson Title Here Try This: 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 6 is a factor 6 times. Insert Lesson Title Here 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 Insert Lesson Title Here Try This: Example 2 Find each value. A. 34 34 = 3 3 3 3 = 81 B. 25 25 = 2 2 2 2 2 = 32 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. 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 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 x 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 Look Back 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. 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 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 Look Back Drawing a diagram helps you see how to use exponents to solve the problem. Insert Lesson Title Here 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 Try this! Write the value of 24: in expanded form? 16 Write 54 in in expanded form? 5x5x5x5 Write 92 in standard form! 18 81