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Exponents and Writing Numbers in Exponential Form

Learn how to represent numbers using exponents and write expressions in exponential form. Practice finding values of numbers in exponential form and solve problem-solving applications involving exponents.

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Exponents and Writing Numbers in Exponential Form

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

  2. 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

  3. 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

  4. Learn to represent numbers by using exponents.

  5. Vocabulary exponent base exponential form

  6. Exponent Base 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. 73 = 7  7  7= 343

  7. 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 54 5 is a factor 4 times. 35 3 is a factor 5 times.

  8. Check It Out: Example 1 Write each expression in exponential form. A. 7  7  7 B. 6  6  6  6  6  6 73 7 is a factor 3 times. 66 6 is a factor 6 times.

  9. Additional Example 2: Finding the Value of Numbers in Exponential Form Find each value. A. 26 B. 45 26 = 2  2  2  2  2  2 = 64 45 = 4  4  4  4  4 = 1,024

  10. Check It Out: Example 2 Find each value. A. 34 B. 25 34 = 3  3  3  3 = 81 25 = 2  2  2  2  2 = 32

  11. 1 Understand the Problem 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? • 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.

  12. Make a Plan 2 You can draw a diagram to see how many calls are in each round. Secretary 1st round – 4 calls 2nd round–16 calls

  13. 3 Solve 4 Look Back 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. Drawing a diagram helps you see how to use exponents to solve the problem.

  14. 1 Understand the Problem 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? • 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.

  15. Make a Plan 2 You can draw a diagram to see how many calls are in each round. Secretary 1st round – 3 calls 2nd round–9 calls

  16. 3 Solve 4 Look Back 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. Drawing a diagram helps you see how to use exponents to solve the problem.

  17. Lesson Quiz Write each expression in exponential form. 1. 12  12  12 2. 9  9  9  9  9  9  9 Find each value. 3. 2024. 64 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? 123 97 1,296 400 243

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