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Name Lesson 11.7 Exponents and Square Numbers Write in exponent form. Then find the value. 1. 5 5 5 2. 2 2 3. 8 8 8 8 4. 4 4 4 4 4 Find the value. 5. 122 10. 83 6. 55 7. 73 8. 18 11. 46 12. 32 13. 113 9. 115 14 57 Compare. Write ,, ., or ⴝ. 15. 53 23 16. 22 41 17. 54 78 18. 62 93 Problem Solving and Test Prep USE DATA For 19–20, use the pattern in the table. 19. James earned 729 pennies. How many plates did James wash in all? Pennies Earned 20. What number in exponent form represents the number of pennies James would earn for washing 11 plates? How many pennies would he earn for washing 11 plates? 21. Which is greater than 92? Number of plates washed Pennies Exponent form Start 1 30 1 3 31 2 9 32 3 27 33 22. What is the greatest square number that is even and is less than 300? What is the value of this square number? A 2 7 43 C 52 D 41 B PW71 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C11_L07.indd PW71 6/28/07 1:12:26 PM Name Lesson 11.7 53; 125 3. 8 8 8 8 22 ; 4 4. 4 4 4 4 4 45; 1,024 84; 4,096 6. 55 144 10. 83 7. 73 8. 18 13. 113 9 4,096 . 23 16. 22 2ⴛ2ⴛ 5ⴛ5 161,051 1 12. 32 2ⴛ2 14 57 1,331 78,125 Compare. Write ,, ., or ⴝ. 15. 53 Check diagram. 41 17. 54 , 78 18. 62 , 5 ⴛ 31 3ⴛ7 Rewrite the prime factorization by using exponents. 6. 2 5 7 2 ⴝ 5. 21 9. 115 343 3,125 11. 46 512 prime factorization of 48. Write the prime factorizaton. Find the prime factorization. You may use a factor tree. 2. 4 3. 100 4. 155 Find the value. 5. 122 2ⴛ2 ⴛ2ⴛ 6 1. Draw a factor tree to find the Write in exponent form. Then find the value. 2. 2 2 Lesson 11.8 Prime Factorization Exponents and Square Numbers 1. 5 5 5 Name 7. 3 3 7 3 7 22 ⴛ 5 ⴛ 7 93 8. 19 19 19 19 3 3 ⴛ 72 194 Find the number for each prime factorization. 9. 3 73 Problem Solving and Test Prep 10. 5 5 5 3 1,029 USE DATA For 19–20, use the pattern in the table. 19. James earned 729 pennies. How many 13. 11 2 2 plates did James wash in all? Pennies Earned 6 plates 20. What number in exponent form represents the number of pennies James would earn for washing 11 plates? How many pennies would he earn for washing 11 plates? 14. 82 23 48 Number of plates washed Pennies Exponent form Start 1 30 1 3 31 2 9 3 2 3 27 33 17. The prime factors of a number are the factors of 36? that is even and is less than 300? What is the value of this square number? B number are 2, 7, and 3. Two is repeated once. What is Patrick’s favorite number? 84 A 20. What is the least number that is the product of two different primes that are squared? A 2 and 3 B 11 and 3 C 5 and 2 36 D 4 and 13 172; 289 Circled problems are suggested homework problems. Circled problems are suggested homework problems. Practice PW71 250 18. The prime factors of Patrick’s favorite first four prime numbers. No factor is repeated. What is the number? 22. What is the greatest square number 43 C 52 D 41 16. 2 5 5 5 1,944 512 210 A 27 76 15. 32 63 19. Which numbers are two of the prime A 12. 2 2 19 3,025 Problem Solving and Test Prep 311; 177,147 pennies 21. Which is greater than 92? 11. 52 112 375 PW72 © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C11_L07.indd PW71 6/28/07 1:12:26 PM MXENL08AWK5X_PHTE_C11_L08.indd PW72 Lesson 11.7 Item Practice © Harcourt • Grade 5 6/15/07 2:25:34 PM Lesson 11.8 Suggested rationale 1 write 5 to the 3rd power in exponent form and find the value 2 write 2 to the 2nd power in exponent form and find the value 5 find the value of a squared number 9 find the value of 11 to the 5th power 20 use exponents to solve a word problem 21 find a number in exponent form that is greater than 9² Item Suggested rationale 2 has 2 prime factors 6 one prime factor is squared 7 one prime factor is squared, the other prime factor is cubed 10 multiply to find the number for the prime factorization 11 multiply to find the number for the prime factorization when the prime factors are written in exponent form 13 find the product 17 use logical reasoning to solve a word problem 20 test prep PW71-PW72 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_RatA.indd PW72 7/2/07 3:02:23 PM