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EXPONENTS

EXPONENTS. WARM-UP Estimate the Following. 3000. 2,129 + 998 = 31, 231 – 1,232 = Round the Following Numbers to the 1000’s place 3) 34,498 4) 134,556. 30,000. 34,000. 135,000. Do you remember “learning your doubles” when you were in 1 st grade?

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EXPONENTS

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  1. EXPONENTS

  2. WARM-UP Estimate the Following 3000 • 2,129 + 998 = • 31, 231 – 1,232 = Round the Following Numbers to the 1000’s place 3) 34,498 4) 134,556 30,000 34,000 135,000

  3. Do you remember “learning your doubles” when you were in 1st grade? 2 + 2 = 3 + 3 = 4 + 4 = 5 + 5 = And so on….

  4. Do you remember “learning your doubles” when you were in 1st grade? How about this? 2 x 2 = 3 x 3 = 4 x 4 = 5 x 5 = And so on….

  5. 9 x 3 9 3 x 3 x 3 27 3. 2  2  2  2 16 4. 5  5  5  5 625

  6. TRY THESE! Multiply. 1.3  3  3 27 2. 2  2  2 8 32 3. 2  2  2  2 x 2 4. 5  5  5 125

  7. SAME THING??? Multiply. 1.3  3  3 27 2. 2  2  2 8 32 3. 2  2  2  2 x 2 4. 5  5  5 125

  8. Learn to represent numbers by using exponents.

  9. Insert Lesson Title Here Vocabulary exponent base exponential form

  10. 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

  11. You Try This One! 25 = 2x2x2x2x2 32!

  12. WARM-UP 16 Because 2 x 2 x 2 x 2 Write the value of 24:in standard form? Write 54 in in expanded form? 5 x 5 x 5 x 5 Write 92 in standard form! 18 81 Write the value of 32:in standard form? 9 6 ?

  13. E X P O N E NT S Write43 in expanded form? 4 x 4 x 4 Write43 in standard form? 64

  14. NEVERAdd the numbers!

  15. E X P O N E NT S Write24 in expanded form? 2 x 2 x 2 x 2 Write24 in standard form? 16

  16. NEVERMultiply the Exponent by the Base!

  17. Insert Lesson Title Here 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.

  18. Insert Lesson Title Here Try This: 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.

  19. Insert Lesson Title Here 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

  20. Insert Lesson Title Here Try This: Example 2 Find each value. A. 34 B. 25 34 = 3  3  3  3 = 81 25 = 2  2  2  2  2 = 32

  21. 1 Understand the Problem 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.

  22. 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

  23. 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 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. Drawing a diagram helps you see how to use exponents to solve the problem.

  24. 1 Understand 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? • 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.

  25. 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

  26. 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.

  27. Insert Lesson Title Here 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

  28. Try this! Write the value of 24:in expanded form? 16 Write 54 in in expanded form? 5 x 5 x 5 x 5 Write 92 in standard form! 18 81

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