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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 1-3 1-4 Exponents Order of Operations Warm Up Problem of the Day Lesson Presentation Course Course 11 1-3 Exponents Warm Up Perform the operations in order from left to right. 1. 2. 3. 4. Course 1 8+4–2 93+1 7–3+5 20 ÷ 4 + 6 10 28 9 11 1-3 Exponents Problem of the Day 0123456789=1 Put the appropriate plus or minus signs between the numbers so that the total equals 1. 0 + 1 – 23 + 45 + 67 – 89 = 1 Course 1 1-3 Exponents Learn to use the order of operations. Course 1 1-3 Exponents Vocabulary numerical expressions evaluate order of operations Course 1 1-3 Exponents A numerical expression is a mathematical phrase that includes only numbers and operation symbols. Numerical 4+8÷2 Expressions 6 371 – 203 + 2 5,006 19 When you evaluate a numerical expression, you find its value. Course 1 1-3 Exponents When an expression has more than one operation, you must know which operation to do first. To make sure that everyone gets the same answer, we use the order of operations. ORDER OF OPERATIONS 1. Perform operations in parentheses. 2. Find the values of numbers with exponents. 3. Multiply or divide from left to right as ordered in the problem. 4. Add or subtract from left to right as ordered in the problem. Course 1 1-3 Exponents Helpful Hint The first letters of these words can help you remember the order of operations. Course 1 Please Parentheses Excuse Exponents My Multiply Dear Divide Aunt Add Sally Subtract 1-3 Exponents Additional Example 1A: Using the Order of Operations Evaluate the expression. 15 – 10 ÷ 2 15 – 10 ÷ 2 There are no parentheses or exponents. 15 – Divide. 5 10 Course 1 Subtract. 1-3 Exponents Additional Example 1B: Using the Order of Operations Evaluate the expression. 9 + (21 ÷ 7) 5 9 + (21 ÷ 7) 5 9+ 9+ 24 Course 1 3 5 15 Perform operations within parentheses. Multiply. Add. 1-3 Exponents Check It Out: Example 1A Evaluate the expression. 12 – 6 ÷ 2 12 – 6 ÷ 2 There are no parentheses or exponents. 12 – Divide. 9 Course 1 3 Subtract. 1-3 Exponents Check It Out: Example 1B Evaluate the expression. 7 + (24 ÷ 6) 3 7 + (24 ÷ 6) 3 7+43 Perform operations within parentheses. 7 + 12 Multiply. 19 Course 1 Add. 1-3 Exponents Additional Example 2A: Using the Order of Operations with Exponents Evaluate the expression. 24 + 6 4 2 +64 There are no parentheses. 16 + 6 4 Find the value of the number with the exponent. 16 + 24 Multiply. 4 40 Course 1 Add. 1-3 Exponents Additional Example 2B: Using the Order of Operations with Exponents Evaluate the expression. 24 ÷ (9 – 6) 32 – 10 24 ÷ (9 – 6) 32 – 10 Perform operations within 24 ÷ 3 32 – 10 parentheses. Find the value of the 24 ÷ 3 9 – 10 number with the exponent. 8 9 – 10 Divide. 72 – 10 62 Course 1 Multiply. Subtract. 1-3 Exponents Check It Out: Example 2A Evaluate the expression. 42 + 3 7 42 + 3 7 There are no parentheses. 16 + 3 7 Find the value of the number with the exponent. 16 + 21 Multiply. 37 Course 1 Add. 1-3 Exponents Check It Out: Example 2B Evaluate the expression. 32 ÷ (8 – 4) 22 – 12 32 ÷ (8 – 4) 22 – 12 32 ÷ 4 22 – 12 32 ÷ 4 4 – 12 8 Course 1 4 – 12 Perform operations within parentheses. Find the value of the number with the exponent. Divide. 32 – 12 Multiply. 20 Subtract. 1-3 Exponents Additional Example 3: Consumer Application Mr. Kellett bought 6 used CDs for $4 each and 5 used CDs for $3 each. Evaluate the following expression to find the amount Mr. Kellett spent on CDs. 64+53 24 + 15 39 Mr. Kellett spent $39 on CDs. Course 1 1-3 Exponents Check It Out: Example 3 Ms. Nivia bought 4 new CDs for $8 each and 6 used CDs for $4 each. Evaluate the following expression to find the amount Ms. Nivia spent on CDs. 48+64 32 + 24 56 Ms. Nivia spent $56 on CDs. Course 1 1-3 Exponents Lesson Quiz Evaluate each expression. 1. 15 + 4 2 23 2. (12 – 5)2 – 10 39 3. 3 + 9 2 – 5 16 4. 43 – 30 ÷ 2 49 5. Chaz bought 4 football cards for $2 each and 8 baseball cards for $3 each. Evaluate the expression to find the amount Chaz spent on cards: 4 2 + 8 3. $32 Course 1