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 an am + n 42 45 42+5 or 47 When dividing powers with the same base, subtract the exponents. Symbols Example

am 56 am n, where a 0 56 2 or 54 an 52

Example 1 Find 2a2(3a). Express your answer using exponents.

2a2(3a) (2 3)(a2 a) Use the Commutative and Associative Properties. (6)(a2 1) The common base is a.

6a3 Add the exponents.

Example (Ϫ8)4 2 Find . Express your answer using exponents. (Ϫ8)2 (8)4 (8)4 2 The common base is 8. (8)2 (8)2 Subtract the exponents.

Exercises

Find each product or quotient. Express your answer using exponents.

1. 47 46 413 2. v5 v4 v 9 3. ( f 3)( f 9) f 12

4. 225 225 2210 5. 7h(5h3) 35h 4 6. 10x2(7x3) Ϫ70x 5

75 18 (12)3 7. 73 8. 12 9. (Ϫ12)0 or 1 72 16 (12)3

c20 (p)18 10. 38 33 311 11. c 7 12. (Ϫp)6 c13 (p)12

2w3 13. 7u6(6u5) 42u11 14. w 2 15. 5m3(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

Find each product or quotient. Express your answer using exponents.

1. 23 25 28 2. 102 107 109

3. 14 1 15 4. 63 63 66 Lesson 4-6 5. (3) 2 (3)3 (Ϫ3)5 6. (9)2(9)2 (Ϫ9)4

7. a2 a3 a 5 8. n8 n3 n11

9. ( p4)(p4) p 8 10. (z6)(z7) z 13

11. (6b3)(3b4) 18b7 12. (v)3(v)7 (Ϫv)10

13. 11a2 3a6 33a 8 14. 10t2 4t10 40t 12

15. (8c2)(9c) 72c 3 16. (4f 8)(5f 6) 20f 14

510 106 17. 58 18. 104 52 102 79 128 19. 73 20. 125 76 123 1009 (2)3 21. 1001 or 100 22. (Ϫ2) 2 1008 2

r8 z10 23. r 1 or r 24. z 2 r7 z8 q8 g12 25. q 4 26. g 4 q4 g8

(y)7 (z)12 27. (Ϫy) 5 28. (Ϫz)7 (y)2 (z)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

Find each product or quotient. Express your answer using exponents.

1. 42 43 4 5 2. 98 96 914

3. 74 72 76 4. 132 134 136

5. (8)5(8)3 (Ϫ8)8 6. (21)9(21)5 (Ϫ21)14

7. t9 t3 t 12 8. h4 h13 h17

9. (m6)(m6) m 12 10. (u11)(u10) u 21

11. (r)7(r)20 (Ϫr)27 12. (w)(w)9 (Ϫw)10

13. 4d5 8d6 32d 11 14. 7j50 6j50 42j 100

15. 5b9 6b2 Ϫ30b11 16. 121 122 123

611 153 17. 68 18. 151 or 15 63 152

99 184 19. 92 20. 18 0 or 1 97 184

(7)6 9521 21. (Ϫ7)1 or Ϫ7 22. 953 (7)5 9518

v30 n19 23. v10 24. 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

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

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. } } 68 18. } } 151 or 15 63 152 15. (8c2)(9c) 72c 3 16. (4f 8)(5f 6) 20f 14 A15 (Lesson 4-6) 99 184 }} 2 } } 0 510 106 19. 7 9 20. 4 18 or 1 17. } } 58 18. } } 104 9 18 52 102 (2 7)6 1 9521 3 79 3 128 5 21. } } ( 7) or 7 22. } } 95 19. }} 7 20. } } 12 (2 7)5 9518 76 123 v30 n19 1009 1 (2 2)3 2 } } 10 } } 8 21. } } 100 or 100 22. } } ( 2) 23. 20 v 24. 11 n 1008 2 2 v n 25. the product of five cubed and five to the fourth power 57 r8 1 z10 2 23. }} r or r 24. } } z r7 z8 26. the quotient of eighteen to the ninth power and eighteen squared 187 q8 g12 }} 4 } } 4 25. 4 q 26. 8 g q g 27. the product of z cubed and z cubed z 6 (2 y)7 (2 z)12 27. } } ( y) 5 28. } } ( z)7 2 (2 y)2 (2 z)5 28. the quotient of x to the fifth power and x cubed x 29. SOUND Decibels are units used to measure sound. The softest sound that can be heard 29. the product of two squared and two to the sixth power 28 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 4 30. the quotient of ten to the seventh power and ten cubed 10 decibels (or a relative loudness of 1012). How many times greater is the relative Glencoe Pre-Algebra loudness of a rock concert than the relative loudness of ordinary conversation? 106 or 31. the product of y squared and y cubed y 5 1,000,000 times

32. the quotient of a to the twentieth power and a to the tenth power a10

Answers