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4. Example 4-1a Objective Use powers and exponents in expressions

5. Example 4-1a Vocabulary Exponent The number of times the base is used as a factor 3 4 4 is the exponent telling you to multiply the base (3) times itself four times 3 · 3 · 3 · 3

6. Example 4-1a Vocabulary Base The number used as a factor 3 4 3 is the base and you will multiply it times itself (factor) 3 · 3 · 3 · 3

7. Example 4-1a Vocabulary Power Number expressed using exponents 3 4 Three to the power of 4 3 · 3 · 3 · 3

8. Example 4-1a Vocabulary Squared The exponent representing the power of 2 3 2 This is read “three squared” 3 · 3

9. Example 4-1a Vocabulary Cubed The exponent representing the power of 33 This is read “three cubed” 3 · 3 · 3

10. Lesson 4 Contents Example 1Write Powers and Products Example 2Write Powers and Products Example 3Use Powers to Solve a Problem Example 4Write Prime Factorization Using Exponents

11. Example 4-1a Write using an exponent. Then find the value of the power. Write the problem Since 5 is repeated with multiplication, write it as the base 1/4 5  5  5  5 5 The 5 is repeated four times, so write the exponent as 4 4 Now solve using the calculator

12. Example 4-1a Write using an exponent. Then find the value of the power. Answer: 625 yxyx The base is 5 so put 5 in the calculator Push the y x key on the calculator 1/4 5  5  5  5 5 The exponent is 4 so put 4 in the calculator 4 Push the = sign on the calculator 54 =

13. Example 4-1b Write using an exponent. Then find the value of the power. 1/4 4747 Answer: ; 16,384

14. Example 4-2a Write as a product. Then find the value of the product. Answer: 512 First write the product which means use multiplication signs Write problem 2/4 8383 The base is 8 so it will be repeated The exponent is 3 so repeat the 8 three times Now solve using the calculator

15. Example 4-2b Write as a product. Then find the value of the product. 2/4 Answer: 6  6  6  6 ; 1,296

16. Example 4-3a Answer: 4,096 meters. ELEVATIONS The highest point in Utah is King’s Peak. It stands just a bit higher than meters. What is this elevation? Write problem 4646 Use calculator to solve 3/4

17. Example 4-3b SWIMMING POOL The length of a new swimming pool being built at the community recreation center is listed as feet. What is the length of the new pool? 3/4 Answer: 64 feet

18. Example 4-4a Write the prime factorization of 126 using exponents. 4/4 126 Write the number Draw prime factorization brackets Decide on a prime number that will go evenly into 126 The one’s digit is 6 which is divisible by 2 Place the prime number 2 to the left of the bracket 2

19. Example 4-4a Write the prime factorization of 126 using exponents. 4/4 1262 Divide 126 by 2 and place the answer below the bracket 63 Determine if 63 is a prime number Since 63 is not an even number, try the divisibility rule for the prime number 3 6 + 3 = 9 and 9 is divisible by 3 so 63 is divisible by 3

20. Example 4-4a Write the prime factorization of 126 using exponents. 4/4 1262 63 63 is not prime so place another prime factorization bracket under 63 Since 63 is divisible by 3, place the 3 to the left of the bracket 3 Divide 63 by 3 and place the answer below the bracket 21 Determine if 21 is a prime number

21. Example 4-4a Write the prime factorization of 126 using exponents. 4/4 1262 63 3 21 Since 21 is not an even number, try the divisibility rule for the prime number 3 2 + 1 = 3 and 3 is divisible by 3 so 21 is divisible by 3 21 is not prime so place another prime factorization bracket under 21 Since 21 is divisible by 3, place the 3 to the left of the bracket 3

22. Example 4-4a Write the prime factorization of 126 using exponents. 4/4 1262 63 3 213 Divide 21 by 3 and place the answer below the bracket 7 Determine if 7 is a prime number The factors of 7 are 1 and 7 7 fits the definition of a prime number Finished prime factoring so now write answer using exponents

23. Example 4-4a Write the prime factorization of 126 using exponents. 4/4 1262 63 3 213 7 Write the smallest prime number which in this case is 2 2 Circle all the 2’s that were used in prime factoring, counting as you go Since there is only 1 two, do not put an exponent

24. Example 4-4a Write the prime factorization of 126 using exponents. 4/4 1262 63 3 213 7 2 Next put a multiplication sign  Note: Do not use “x” for multiplication Write the next smallest prime number which in this case is 3 Circle all the 3’s that were used in prime factoring, counting as you go 3

25. Example 4-4a Write the prime factorization of 126 using exponents. 4/4 1262 63 3 213 7 2  Since there are 2 threes, put an exponent of 2 3 2 Next put a multiplication sign  Write the next smallest prime number which in this case is 7 7

26. Example 4-4a Write the prime factorization of 126 using exponents. 4/4 1262 63 3 213 7 2  3 2  7 Circle all the 7’s that were used in prime factoring, counting as you go Since there is only 1 seven, do not put an exponent Answer:

27. Example 4-4b Write the prime factorization of 144 using exponents. * 4/4 Answer: 2 4  3 2

28. End of Lesson 4 Assignment Lesson 1:4Powers & Exponents11 - 34 All