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? ,

Course Exponents 1-4 Order of Operations Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Course Exponents Warm Up Perform the operations in order from left to right –  – ÷

Course Exponents Problem of the Day = 1 Put the appropriate plus or minus signs between the numbers so that the total equals – – 89 = 1

Course Exponents Learn to use the order of operations.

Course Exponents Vocabulary numerical expressions evaluate order of operations

Course Exponents A numerical expression is a mathematical phrase that includes only numbers and operation symbols. Numerical Expressions ÷ 2  – ,006  19 When you evaluate a numerical expression, you find its value.

Course 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 Exponents The first letters of these words can help you remember the order of operations. PleaseParentheses ExcuseExponents MyMultiply DearDivide AuntAdd SallySubtract Helpful Hint

Course Exponents Additional Example 1A: Using the Order of Operations Evaluate the expression. There are no parentheses or exponents. 15 – 5 Divide. 10 Subtract. 15 – 10 ÷ 2

Course Exponents Additional Example 1B: Using the Order of Operations Evaluate the expression. 9 + (21 ÷ 7)  5 Perform operations within parentheses. Multiply  Add. 24

Course Exponents Check It Out: Example 1A Evaluate the expression. There are no parentheses or exponents. 12 – 3 Divide. 9 Subtract. 12 – 6 ÷ 2

Course Exponents Check It Out: Example 1B Evaluate the expression. 7 + (24 ÷ 6)  3 Perform operations within parentheses. Multiply  Add. 19

Course Exponents Additional Example 2A: Using the Order of Operations with Exponents Evaluate the expression  4 There are no parentheses.Multiply  Add  4 4 Find the value of the number with the exponent.

Course Exponents Additional Example 2B: Using the Order of Operations with Exponents Evaluate the expression. 24 ÷ (9 – 6)  3 2 – 10 Perform operations within parentheses. Multiply. 8  9 – – 10 Divide. 62 Find the value of the number with the exponent. 24 ÷ (9 – 6)  3 2 – 1024 ÷ 3  3 2 – ÷ 3  9 – 10 Subtract.

Course Exponents Check It Out: Example 2A Evaluate the expression  7 There are no parentheses.Multiply  Add  7 Find the value of the number with the exponent.

Course Exponents Check It Out: Example 2B Evaluate the expression. 32 ÷ (8 – 4)  2 2 – 12 Perform operations within parentheses. Multiply. 8  4 – – 12 Divide. 20 Find the value of the number with the exponent. 32 ÷ (8 – 4)  2 2 – ÷ 4  2 2 – ÷ 4  4 – 12 Subtract.

Course 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. 6   Mr. Kellett spent $39 on CDs.

Course 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. 4   Ms. Nivia spent $56 on CDs.

Course Exponents Lesson Quiz Evaluate each expression  2 2. (12 – 5) 2 –  2 – – 30 ÷ 2 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   $32