3. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN
4. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent base
5. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 base
6. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 base
7. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2 base
8. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) base
9. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 base
10. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 base
11. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) base
12. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base
13. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base
14. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base Rules of Exponents
15. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base Rules of Exponents Multiplication Rule: ANAK =AN+K
16. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base Rules of Exponents Multiplication Rule: ANAK =AN+K Example B. a. 5354
17. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base Rules of Exponents Multiplication Rule: ANAK =AN+K Example B. a. 5354 = (5*5*5)(5*5*5*5)
18. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base Rules of Exponents Multiplication Rule: ANAK =AN+K Example B. a. 5354 = (5*5*5)(5*5*5*5) = 53+4 = 57 b. x5y7x4y6
19. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base Rules of Exponents Multiplication Rule: ANAK =AN+K Example B. a. 5354 = (5*5*5)(5*5*5*5) = 53+4 = 57 b. x5y7x4y6 = x5x4y7y6
20. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base Rules of Exponents Multiplication Rule: ANAK =AN+K Example B. a. 5354 = (5*5*5)(5*5*5*5) = 53+4 = 57 b. x5y7x4y6 = x5x4y7y6 = x9y13
21. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base Rules of Exponents Multiplication Rule: ANAK =AN+K Example B. a. 5354 = (5*5*5)(5*5*5*5) = 53+4 = 57 b. x5y7x4y6 = x5x4y7y6 = x9y13 AN = AN – K Division Rule: AK
22. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base Rules of Exponents Multiplication Rule: ANAK =AN+K Example B. a. 5354 = (5*5*5)(5*5*5*5) = 53+4 = 57 b. x5y7x4y6 = x5x4y7y6 = x9y13 AN = AN – K Division Rule: AK 56 Example C. 52
23. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base Rules of Exponents Multiplication Rule: ANAK =AN+K Example B. a. 5354 = (5*5*5)(5*5*5*5) = 53+4 = 57 b. x5y7x4y6 = x5x4y7y6 = x9y13 AN = AN – K Division Rule: AK 56 (5)(5)(5)(5)(5)(5) Example C. = 52 (5)(5)
24. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base Rules of Exponents Multiplication Rule: ANAK =AN+K Example B. a. 5354 = (5*5*5)(5*5*5*5) = 53+4 = 57 b. x5y7x4y6 = x5x4y7y6 = x9y13 AN = AN – K Division Rule: AK 56 (5)(5)(5)(5)(5)(5) Example C. = 52 (5)(5)
25. Exponents We write the quantity A multiplied to itself N times as AN, i.e. A x A x A ….x A = AN exponent Example A. 43 = (4)(4)(4) = 64 (xy)2= (xy)(xy) = x2y2 xy2 = (x)(yy) –x2 = –(xx) base Rules of Exponents Multiplication Rule: ANAK =AN+K Example B. a. 5354 = (5*5*5)(5*5*5*5) = 53+4 = 57 b. x5y7x4y6 = x5x4y7y6 = x9y13 AN = AN – K Division Rule: AK 56 (5)(5)(5)(5)(5)(5) = 56 – 2 = 54 Example C. = 52 (5)(5)
29. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4
30. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320
31. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 A1
32. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 A1
33. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0 A1
34. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1
35. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0
36. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = AK AK
37. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K AK AK
38. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK
39. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK 1 Negative-Power Rule: A–K = , A = 0 AK
40. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK 1 Negative-Power Rule: A–K = , A = 0 AK Example D. Simplify a. 30
41. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK 1 Negative-Power Rule: A–K = , A = 0 AK Example D. Simplify a. 30 = 1
42. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK 1 Negative-Power Rule: A–K = , A = 0 AK Example D. Simplify a. 30 = 1 b. 3–2
43. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK 1 Negative-Power Rule: A–K = , A = 0 AK Example D. Simplify a. 30 = 1 1 b. 3–2 = 32
44. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK 1 Negative-Power Rule: A–K = , A = 0 AK Example D. Simplify a. 30 = 1 1 1 b. 3–2 = = 9 32
45. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK 1 Negative-Power Rule: A–K = , A = 0 AK Example D. Simplify a. 30 = 1 1 1 b. 3–2 = = 9 32 2 c. ( )–1 5
46. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK 1 Negative-Power Rule: A–K = , A = 0 AK Example D. Simplify a. 30 = 1 1 1 b. 3–2 = = 9 32 2 1 c. ( )–1 = = 5 2/5
47. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK 1 Negative-Power Rule: A–K = , A = 0 AK Example D. Simplify a. 30 = 1 1 1 b. 3–2 = = 9 32 2 1 5 5 c. ( )–1 1* = = = 5 2/5 2 2
48. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK 1 Negative-Power Rule: A–K = , A = 0 AK Example D. Simplify a. 30 = 1 1 1 b. 3–2 = = 9 32 2 1 5 5 c. ( )–1 1* = = = 5 2/5 2 2 a b In general ( )–K = ( )K b a
49. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK 1 Negative-Power Rule: A–K = , A = 0 AK Example D. Simplify a. 30 = 1 1 1 b. 3–2 = = 9 32 2 1 5 5 c. ( )–1 1* = = = 5 2/5 2 2 a b In general ( )–K = ( )K b a 2 d. ( )–2 5
50. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK 1 Negative-Power Rule: A–K = , A = 0 AK Example D. Simplify a. 30 = 1 1 1 b. 3–2 = = 9 32 2 1 5 5 c. ( )–1 1* = = = 5 2/5 2 2 a b In general ( )–K = ( )K b a 2 5 d. ( )–2 = ( )2 5 2
51. Exponents Power Rule: (AN)K = ANK Example D. (34)5 = (34)(34)(34)(34)(34)= 34+4+4+4+4 = 34*5 = 320 A1 Since = 1 = A1 – 1 = A0, we obtain the 0-power Rule. A1 0-Power Rule: A0 = 1, A = 0 1 A0 Since = = A0 – K = A–K, we get the negative-power Rule. AK AK 1 Negative-Power Rule: A–K = , A = 0 AK Example D. Simplify a. 30 = 1 1 1 b. 3–2 = = 9 32 2 1 5 5 c. ( )–1 1* = = = 5 2/5 2 2 a b In general ( )–K = ( )K b a 2 25 5 d. ( )–2 = ( )2 = 5 4 2
57. Exponents 1 1 1 1 1 – 1* – = e. 3–1 – 40 * 2–2 = = 3 22 3 4 12 Although the negative power means to reciprocate, for problems of consolidating exponents, we do not reciprocate the negative exponents.
58. Exponents 1 1 1 1 1 – 1* – = e. 3–1 – 40 * 2–2 = = 3 22 3 4 12 Although the negative power means to reciprocate, for problems of consolidating exponents, we do not reciprocate the negative exponents. Instead we add or subtract them using the multiplication and division rules first.
59. Exponents 1 1 1 1 1 – 1* – = e. 3–1 – 40 * 2–2 = = 3 22 3 4 12 Although the negative power means to reciprocate, for problems of consolidating exponents, we do not reciprocate the negative exponents. Instead we add or subtract them using the multiplication and division rules first. Example E. Simplify 3–2 x4 y–6 x–8 y 23
60. Exponents 1 1 1 1 1 – 1* – = e. 3–1 – 40 * 2–2 = = 3 22 3 4 12 Although the negative power means to reciprocate, for problems of consolidating exponents, we do not reciprocate the negative exponents. Instead we add or subtract them using the multiplication and division rules first. Example E. Simplify 3–2 x4 y–6 x–8 y 23 3–2 x4y–6x–8y23
61. Exponents 1 1 1 1 1 – 1* – = e. 3–1 – 40 * 2–2 = = 3 22 3 4 12 Although the negative power means to reciprocate, for problems of consolidating exponents, we do not reciprocate the negative exponents. Instead we add or subtract them using the multiplication and division rules first. Example E. Simplify 3–2 x4 y–6 x–8 y 23 3–2 x4y–6x–8y23 = 3–2 x4 x–8 y–6y23
62. Exponents 1 1 1 1 1 – 1* – = e. 3–1 – 40 * 2–2 = = 3 22 3 4 12 Although the negative power means to reciprocate, for problems of consolidating exponents, we do not reciprocate the negative exponents. Instead we add or subtract them using the multiplication and division rules first. Example E. Simplify 3–2 x4 y–6 x–8 y 23 3–2 x4y–6x–8y23 = 3–2 x4 x–8 y–6y23 1 = x4 – 8y–6+23 9
63. Exponents 1 1 1 1 1 – 1* – = e. 3–1 – 40 * 2–2 = = 3 22 3 4 12 Although the negative power means to reciprocate, for problems of consolidating exponents, we do not reciprocate the negative exponents. Instead we add or subtract them using the multiplication and division rules first. Example E. Simplify 3–2 x4 y–6 x–8 y 23 3–2 x4y–6x–8y23 = 3–2 x4 x–8 y–6y23 1 = x4 – 8y–6+23 = x–4y17 9 1 9
64. Exponents 1 1 1 1 1 – 1* – = e. 3–1 – 40 * 2–2 = = 3 22 3 4 12 Although the negative power means to reciprocate, for problems of consolidating exponents, we do not reciprocate the negative exponents. Instead we add or subtract them using the multiplication and division rules first. Example E. Simplify 3–2 x4 y–6 x–8 y 23 3–2 x4y–6x–8y23 = 3–2 x4 x–8 y–6y23 1 = x4 – 8y–6+23 = x–4y17 = y17 9 1 9 1 9x4
65. Exponents 1 1 1 1 1 – 1* – = e. 3–1 – 40 * 2–2 = = 3 22 3 4 12 Although the negative power means to reciprocate, for problems of consolidating exponents, we do not reciprocate the negative exponents. Instead we add or subtract them using the multiplication and division rules first. Example E. Simplify 3–2 x4 y–6 x–8 y 23 3–2 x4y–6x–8y23 = 3–2 x4 x–8 y–6y23 1 = x4 – 8y–6+23 = x–4y17 = y17 = 9 1 9 1 9x4 y17 9x4
66. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3
67. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3 23x–8 26x–3
68. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3 23x–8 = 23 – 6x–8–(–3 ) 26x–3
69. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3 23x–8 = 23 – 6x–8–(–3 ) 26x–3 = 2–3x–5
70. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3 23x–8 = 23 – 6x–8–(–3 ) 26x–3 = 2–3x–5 1 1 1 = = 23 x5 * 8x5
71. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3 23x–8 = 23 – 6x–8–(–3 ) 26x–3 = 2–3x–5 1 1 1 = = 23 x5 * 8x5 (3x–2y3)–2 x2 Example G. Simplify 3–5x–3(y–1x2)3
72. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3 23x–8 = 23 – 6x–8–(–3 ) 26x–3 = 2–3x–5 1 1 1 = = 23 x5 * 8x5 (3x–2y3)–2 x2 Example G. Simplify 3–5x–3(y–1x2)3 (3x–2y3)–2 x2 3–5x–3(y–1x2)3
73. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3 23x–8 = 23 – 6x–8–(–3 ) 26x–3 = 2–3x–5 1 1 1 = = 23 x5 * 8x5 (3x–2y3)–2 x2 Example G. Simplify 3–5x–3(y–1x2)3 (3x–2y3)–2 x2 3–2x4y–6x2 = 3–5x–3y–3 x6 3–5x–3(y–1x2)3
74. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3 23x–8 = 23 – 6x–8–(–3 ) 26x–3 = 2–3x–5 1 1 1 = = 23 x5 * 8x5 (3x–2y3)–2 x2 Example G. Simplify 3–5x–3(y–1x2)3 (3x–2y3)–2 x2 3–2x4y–6x2 3–2x4x2y–6 = = 3–5x–3y–3 x6 3–5x–3(y–1x2)3 3–5x–3x6y–3
75. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3 23x–8 = 23 – 6x–8–(–3 ) 26x–3 = 2–3x–5 1 1 1 = = 23 x5 * 8x5 (3x–2y3)–2 x2 Example G. Simplify 3–5x–3(y–1x2)3 (3x–2y3)–2 x2 3–2x4y–6x2 3–2x4x2y–6 = = 3–5x–3y–3 x6 3–5x–3(y–1x2)3 3–5x–3x6y–3 3–2x6y–6 = 3–5x3y–3
76. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3 23x–8 = 23 – 6x–8–(–3 ) 26x–3 = 2–3x–5 1 1 1 = = 23 x5 * 8x5 (3x–2y3)–2 x2 Example G. Simplify 3–5x–3(y–1x2)3 (3x–2y3)–2 x2 3–2x4y–6x2 3–2x4x2y–6 = = 3–5x–3y–3 x6 3–5x–3(y–1x2)3 3–5x–3x6y–3 3–2x6y–6 = = 3–2 – (–5) x6 – 3 y–6 – (–3) 3–5x3y–3
77. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3 23x–8 = 23 – 6x–8–(–3 ) 26x–3 = 2–3x–5 1 1 1 = = 23 x5 * 8x5 (3x–2y3)–2 x2 Example G. Simplify 3–5x–3(y–1x2)3 (3x–2y3)–2 x2 3–2x4y–6x2 3–2x4x2y–6 = = 3–5x–3y–3 x6 3–5x–3(y–1x2)3 3–5x–3x6y–3 3–2x6y–6 = = 3–2 – (–5) x6 – 3 y–6 – (–3) 3–5x3y–3 = 33 x3 y–3 =
78. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3 23x–8 = 23 – 6x–8–(–3 ) 26x–3 = 2–3x–5 1 1 1 = = 23 x5 * 8x5 (3x–2y3)–2 x2 Example G. Simplify 3–5x–3(y–1x2)3 (3x–2y3)–2 x2 3–2x4y–6x2 3–2x4x2y–6 = = 3–5x–3y–3 x6 3–5x–3(y–1x2)3 3–5x–3x6y–3 3–2x6y–6 = = 3–2 – (–5) x6 – 3 y–6 – (–3) 3–5x3y–3 27x3 = 33 x3 y–3 = y3
79. Exponents 23x–8 Example F. Simplify using the rules for exponents. Leave the answer in positive exponents only. 26 x–3 23x–8 = 23 – 6x–8–(–3 ) 26x–3 = 2–3x–5 1 1 1 = = 23 x5 * 8x5 (3x–2y3)–2 x2 Example G. Simplify 3–5x–3(y–1x2)3 (3x–2y3)–2 x2 3–2x4y–6x2 3–2x4x2y–6 = = 3–5x–3y–3 x6 3–5x–3(y–1x2)3 3–5x–3x6y–3 3–2x6y–6 = = 3–2 – (–5) x6 – 3y–6 – (–3) 3–5x3y–3 27x3 = 33 x3 y–3 = y3