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Warm-up: 1.) 2 x 2 x 2 =8 2.) 5 x 5 =25 3.) 4 x 4 x 4 =64 4.) 10 x 10 x 10 =1000

Warm-up: 1.) 2 x 2 x 2 =8 2.) 5 x 5 =25 3.) 4 x 4 x 4 =64 4.) 10 x 10 x 10 =1000. Remember that any number can be written as a product of Prime Factors. Example: 32. 2. 16. 2. 2. 8. 2. 2. 2. 4. 2. 2. 2. 2. 2.

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Warm-up: 1.) 2 x 2 x 2 =8 2.) 5 x 5 =25 3.) 4 x 4 x 4 =64 4.) 10 x 10 x 10 =1000

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  1. Warm-up: 1.) 2 x 2 x 2 =8 2.) 5 x 5 =25 3.) 4 x 4 x 4 =64 4.) 10 x 10 x 10 =1000 CONFIDENTIAL

  2. Remember that any number can be written as a product of Prime Factors. Example: 32 2 16 2 2 8 2 2 2 4 2 2 2 2 2 The Number 32 can be written as 2 x 2 x 2 x 2 x 2 CONFIDENTIAL

  3. Example: 32 2 16 2 2 8 2 2 2 4 2 2 2 2 2 The Number 32 can be written as 2 x 2 x 2 x 2 x 2 A product of prime numbers can be expressed using EXPONENTS and a BASE 25 CONFIDENTIAL

  4. Numbers expressed using Exponents are called Powers CONFIDENTIAL

  5. There are several symbols you might see for Multiplication 2 x 2 x 2 = 23 2 * 2 * 2 = 23 . . 2 2 2 = 23 CONFIDENTIAL

  6. Let's Practice... If we write 3 x 3 x 3 x 3 using an exponent, the base is 3 AND the exponent is 4 . . . 3 3 3 3 = 34 = 81 CONFIDENTIAL

  7. We can also refer to writing 45 as a PRODUCT OF THE SAME FACTOR (Remember that a "Product" is the answer to a multiplication problem.) The Base is 4. The Exponent is 5. So 4 is a Factor 5 times. 45 = 4 x 4 x 4 x 4 x 4 = 1,024 CONFIDENTIAL

  8. Your Turn! Write 7 x 7 x 7 using an Exponent. Then find its value. 73 = 343 CONFIDENTIAL

  9. Write 23 as a product of the same factor. Then find its value. 2 x 2 x 2 = 8 CONFIDENTIAL

  10. Exponents can be used to write the Prime Factorization of a number. Example: 24 x 2 12 x x 2 2 6 OR x x 2 2 2 x 3 23 x 3 (Start with the smallest prime factor) CONFIDENTIAL

  11. Your Turn! Write the Prime Factorization of the number using Exponents. 90 x 2 45 x x 2 3 15 OR x x 3 2 3 x 5 2 x 32 x 5 CONFIDENTIAL

  12. Your Turn! Write the Prime Factorization of the number using Exponents. 120 x 2 60 x x 2 2 30 OR x x 2 2 2 x 15 23 x 3 x 5 x x 2 2 2 x 3 x 5 CONFIDENTIAL

  13. Any number to the 1 power equals itself. Example: 101 = 10 51 = 5 2,3451 = 2,345 Any number to the 0 power equals 1. Example: 100 = 1 50 = 1 2,3450 = 1 CONFIDENTIAL

  14. Practice Problems: Write each product using an exponent. Then find its value. 1.) 2 x 2 x 2 x 2 = 24 = 16 2.) 6 x 6 x 6 = 63 = 216 Write each power as a product of the same factor. Then find its value. 3.) 26 = 2 x 2 x 2 x 2 x 2 x 2 = 64 4.) 34 = 3 x 3 x 3 x 3 = 81 Write the prime factorization of this number using exponents. 5.) 48 48 x 2 24 24 x 3 x x 2 2 12 OR x x 2 2 2 x 6 CONFIDENTIAL x x 2 2 2 x 2 x 3

  15. 6.) Find the value of 51 = 5 7.) Find the value of 2360 = 1 CONFIDENTIAL

  16. Write the values for these powers of 10. a) 101 = 10 b) 102 = 100 c) 103 = 1,000 d) 104 = 10,000 e) 105 = 100,000 f) Describe the pattern for the powers of 10. The next value is found by dividing the previous power by 10 CONFIDENTIAL

  17. An estimated 109 people in the world speak Mandarin Chinese. About how many people speak this language? 109 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000,000 CONFIDENTIAL

  18. Let's see how well we know Powers and Exponents! 1. Can you write this product using an exponent? 6 x 6 x 6 x 6 = 64 2. Can you find the value of this product? 5 x 5 x 5 = 53 = 125 3. Can you write this power as a product of the same factor? 36 = 3 x 3 x 3 x 3 x 3 x 3 4. Can you find the value of this power? 24 = 2 x 2 x 2 x2 CONFIDENTIAL

  19. 5. Can you find the value of this power? 570 = 1 6. Find the prime factorization of this number using exponents. 20 22 x 5 OR x 2 10 x x 2 2 5 CONFIDENTIAL

  20. Well Done!! We learned that POWERS are numbers expressed using exponents. 34 We learned that a product of prime factors can be written using a Base and Exponents. 23 = 2 x 2 x 2 = 8 We learned how to find the value of 43 4 x 4 x 4 = 64 We learned how to write the Prime Factorization of a number using exponents. 24 = 2 x 2 x 2 x 3 = 23 x 3 CONFIDENTIAL

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