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Skills Practice Multiplying and Dividing Monomials NAME ______________________________________________ DATE ______________ PERIOD _____ 4-6 Study Guide and Intervention Multiplying and Dividing Monomials When multiplying powers with the same base, add the exponents. Symbols Example am и an ϭ am + n 42 и 45 ϭ 42+5 or 47 When dividing powers with the same base, subtract the exponents. Symbols Example am 56 Ϫ ᎏᎏ ϭ am n, where a 0 ᎏᎏ ϭ 56 2 or 54 an 52 Example 1 Find 2a2(3a). Express your answer using exponents. 2a2(3a) ϭ (2 и 3)(a2 и a) Use the Commutative and Associative Properties. (6)(a2 1) The common base is a. ϭ 6a3 Add the exponents. Example (Ϫ8)4 2 Find ᎏᎏ. Express your answer using exponents. (Ϫ8)2 (Ϫ8)4 Ϫ ᎏᎏ ϭ (Ϫ8)4 2 The common base is Ϫ8. (Ϫ8)2 ϭ (Ϫ8)2 Subtract the exponents. Exercises Find each product or quotient. Express your answer using exponents. 1. 47 и 46 413 2. v5 и v4 v 9 3. ( f 3)( f 9) f 12 4. 225 225 2210 5. 7h(5h3) 35h 4 6. Ϫ10x2(7x3) Ϫ70x 5 75 18 (Ϫ12)3 7. ᎏᎏ 73 8. ᎏᎏ 12 9. ᎏᎏ (Ϫ12)0 or 1 72 16 (Ϫ12)3 c20 (Ϫp)18 10. 38 и 33 311 11. ᎏᎏ c 7 12. ᎏᎏ (Ϫp)6 c13 (Ϫp)12 2w3 13. Ϫ7u6(Ϫ6u5) 42u11 14. ᎏᎏ w 2 15. Ϫ5m3(4m6) Ϫ20m9 2w 16. the product of two cubed and two squared 25 17. the quotient of six to the eighth power and six squared 66 © Glencoe/McGraw-Hill 190 Glencoe Pre-Algebra NAME ______________________________________________ DATE ______________ PERIOD _____ 4-6 Skills Practice Multiplying and Dividing Monomials Find each product or quotient. Express your answer using exponents. 1. 23 и 25 28 2. 102 и 107 109 3. 14 и 1 15 4. 63 и 63 66 Lesson 4-6 5. (Ϫ3) 2 (Ϫ3)3 (Ϫ3)5 6. (Ϫ9)2(Ϫ9)2 (Ϫ9)4 7. a2 и a3 a 5 8. n8 и n3 n11 9. ( p4)(p4) p 8 10. (z6)(z7) z 13 11. (6b3)(3b4) 18b7 12. (Ϫv)3(Ϫv)7 (Ϫv)10 13. 11a2 и 3a6 33a 8 14. 10t2 и 4t10 40t 12 15. (8c2)(9c) 72c 3 16. (4f 8)(5f 6) 20f 14 510 106 17. ᎏᎏ 58 18. ᎏᎏ 104 52 102 79 128 19. ᎏᎏ 73 20. ᎏᎏ 125 76 123 1009 (Ϫ2)3 21. ᎏᎏ 1001 or 100 22. ᎏᎏ (Ϫ2) 2 1008 Ϫ2 r8 z10 23. ᎏᎏ r 1 or r 24. ᎏᎏ z 2 r7 z8 q8 g12 25. ᎏᎏ q 4 26. ᎏᎏ g 4 q4 g8 (Ϫy)7 (Ϫz)12 27. ᎏᎏ (Ϫy) 5 28. ᎏᎏ (Ϫz)7 (Ϫy)2 (Ϫz)5 29. the product of two squared and two to the sixth power 28 30. the quotient of ten to the seventh power and ten cubed 104 31. the product of y squared and y cubed y 5 32. the quotient of a to the twentieth power and a to the tenth power a10 © Glencoe/McGraw-Hill 191 Glencoe Pre-Algebra NAME ______________________________________________ DATE ______________ PERIOD _____ 4-6 Practice Multiplying and Dividing Monomials Find each product or quotient. Express your answer using exponents. 1. 42 и 43 4 5 2. 98 и 96 914 3. 74 и 72 76 4. 132 и 134 136 5. (Ϫ8)5(Ϫ8)3 (Ϫ8)8 6. (Ϫ21)9(Ϫ21)5 (Ϫ21)14 7. t9 и t3 t 12 8. h4 и h13 h17 9. (m6)(m6) m 12 10. (u11)(u10) u 21 11. (Ϫr)7(Ϫr)20 (Ϫr)27 12. (Ϫw)(Ϫw)9 (Ϫw)10 13. 4d5 и 8d6 32d 11 14. 7j50 и 6j50 42j 100 15. Ϫ5b9 и 6b2 Ϫ30b11 16. 121 и 122 123 611 153 17. ᎏᎏ 68 18. ᎏᎏ 151 or 15 63 152 99 184 19. ᎏᎏ 92 20. ᎏᎏ 18 0 or 1 97 184 (Ϫ7)6 9521 21. ᎏᎏ (Ϫ7)1 or Ϫ7 22. ᎏᎏ 953 (Ϫ7)5 9518 v30 n19 23. ᎏᎏ v10 24. ᎏᎏ n 8 v20 n11 25. the product of five cubed and five to the fourth power 57 26. the quotient of eighteen to the ninth power and eighteen squared 187 27. the product of z cubed and z cubed z 6 28. the quotient of x to the fifth power and x cubed x 2 29. SOUND Decibels are units used to measure sound. The softest sound that can be heard is rated as 0 decibels (or a relative loudness of 1). Ordinary conversation is rated at about 60 decibels (or a relative loudness of 106). A rock concert is rated at about 120 decibels (or a relative loudness of 1012). How many times greater is the relative loudness of a rock concert than the relative loudness of ordinary conversation? 106 or 1,000,000 times © Glencoe/McGraw-Hill 192 Glencoe Pre-Algebra © Glencoe/McGraw-Hill NAME ______________________________________________ DATE ______________ PERIOD _____ NAME ______________________________________________ DATE ______________ PERIOD _____ 4-5 Enrichment 4-6 Study Guide and Intervention Multiplying and Dividing Monomials Matching Equivalent Fractions When multiplying powers with the same base, add the exponents. Symbols Example Cut out the pieces below and match the edges so that equivalent fractions meet. m ? n 5 m + n 2 ? 5 5 2+5 7 The pieces form a 4 6 rectangle. The outer edges of the rectangle formed will a a a 4 4 4 or 4 have no fractions. When dividing powers with the same base, subtract the exponents. Symbols Example 12 11 13 12 10 9 8 7 1 9 am 2 56 2 } } 5 m n } } 5 6 2 4 n a , where a 0 2 5 or 5 a 5 Answers 15 155 12 18 3 16 115 8 104 5 14 3 35 9 42 8 28 8 20 7 15 7 Ex ample 1 Find 2a2(3a). Express your answer using exponents. 21 24 10 50 45 45 40 3 3 2 2a2(3a) 5 (2 ?3)(a2 ?a) Use the Commutative and Associative Properties. 11 1 10 9 9 1 8 1 2 1 3 5 (6)(a ) The common base is a. 5 6a3 Add the exponents. (Lessons 4-5and4-6) 15 1 35 7 18 4 8 21 8231945 2 77 13 48 9 10 Ex ample ( 8)4 2 Find } } . Express your answer using exponents. ( 8)2 A14 44 40 56 52 18 33 27 2 (2 8)4 2 } } 5 (2 8)4 2 The common base is 2 8. (2 8)2 12 10 11 8 7 1 1 7 5 (2 8)2 Subtract the exponents. 24 49 6 4 1 9 5 54 2091 24 8 35 133 15 7 7 Exer cises Find each product or quotient. Express your answer using exponents. 33 21 48 44 20 18 2 3 1. 47 ?46 413 2. v5 ?v4 v 9 3. ( f 3)( f 9) f 12 5 1 4 1 6 1 14 13 4. 225 ?225 2210 5. 7h(5h3) 35h 4 6. 2 10x2(7x3) 70x 5 4 3 14 5 2 2 2 6 2211794 56 22 11 8 7 5 75 18 (2 12)3 } } 3 } } 2 } } 0 7. 2 7 8. 6 1 9. 2 3 ( 12) or 1 33 40 35 7 1 ( 12) 9 8 2 c20 (2 p)18 11 11 10 7 6 8 3 11 7 6 3 10. 3 ?3 3 11. } } c 12. } } ( p) 1234 c13 (2 p)12 3 5678 6 5 11 2w 2 3 6 9 2 25 3 3 20 13. 2 7u (2 6u ) 42u 14. } } w 15. 2 5m (4m ) 20m 1 3 45 16 6 6125 32 2w Glencoe Pre-Algebra 9 101112 16. the product of two cubed and two squared 25 20 36 52 48 35 30 6 3 13 14 15 16 17. the quotient of six to the eighth power and six squared 66 17 18 19 20 21 22 23 24 Lesson 4-5 © Glencoe/McGraw-Hill 189 Glencoe Pre-Algebra © Glencoe/McGraw-Hill 190 Glencoe Pre-Algebra © Glencoe/McGraw-Hill NAME ______________________________________________ DATE ______________ PERIOD _____ NAME ______________________________________________ DATE ______________ PERIOD _____ 4-6 Skills Pr actice 4-6 Pr actice Multiplying and Dividing Monomials Multiplying and Dividing Monomials Find each product or quotient. Express your answer using exponents. Find each product or quotient. Express your answer using exponents. 2 ? 3 5 8 ? 6 14 1. 23 ?25 28 2. 102 ?107 109 1. 4 4 4 2. 9 9 9 3. 74 ?72 76 4. 132 ?134 136 3. 14 ?1 15 4. 63 ?63 66 5 3 8 9 5 14 Lesson 4-6 5. (2 8) (2 8) ( 8) 6. (2 21) (2 21) ( 21) 5. (2 3) 2 (2 3)3 ( 3)5 6. (2 9)2(2 9)2 ( 9)4 7. t9 ?t3 t 12 8. h4 ?h13 h17 7. a2 ?a3 a 5 8. n8 ?n3 n11 9. (m6)(m6) m 12 10. (u11)(u10) u 21 4 4 8 6 7 13 9. ( p )(p ) p 10. (z )(z ) z 11. (2 r)7(2 r)20 ( r)27 12. (2 w)(2 w)9 ( w)10 Answers 5 6 11 50 50 100 11. (6b3)(3b4) 18b7 12. (2 v)3(2 v)7 ( v)10 13. 4d ?8d 32d 14. 7j ?6j 42j 15. 2 5b9 ?6b2 30b11 16. 121 ?122 123 13. 11a2 ?3a6 33a 8 14. 10t2 ?4t10 40t 12 611 153 17.
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