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Indecsau

Indecsau. Gallwn ddefnyddio’r ffaith bod a x a = a 2 i symleiddio : a x a x a =. a 3. c x c x c =. c 3. b x b x b x b =. b 4. Hefyd, gallwn ddefnyddio hwn i symleiddio lluoswm sawl term tebyg:. a x a x b x b x b =. a 2 x b 3. a x b x b x b x a =. a 2 x b 3.

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Indecsau

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  1. Indecsau

  2. Gallwn ddefnyddio’r ffaith bod a x a = a2 i symleiddio : a x a x a = a3 c x c x c = c3 b x b x b x b = b4 Hefyd, gallwn ddefnyddio hwn i symleiddio lluoswm sawl term tebyg: a x a x b x b x b = a2 x b3 a x b x b x b x a = a2 x b3 I osgoi cymlethdod yn y dyfodol ysgrifennwn a2 x b3 fel a2 b3, hynny yw heb yr arwydd lluosi.

  3. Ymarfer • Newidiwch y canlynol i’r ffurf indecs: • d x d x d = • e x e x e x e x e x e = • d x d x c x c x c = • a x a x a x d x d = • b x b x a x a x b = • b x b x c x a x c x c x a = • b x a x c x b x c x a x c x c =

  4. RHEOLAU INDECSAU Rheol 1: Lluosi Indecsau Ystyriwn a2 x a3 a x a x a x a x a = a5 b3 x b3 b x b x b x b x b x b = b6 Y rheol gyffredinol: am x an = am + n Rydym ond yn gallu adio’r indecsau pan mae’r llythyren yr un peth

  5. Ymarfer 8. a4 x a7 x a5 9. b7 x b3 x b3 10. c9 x c4 x c-2 11. d-7 x d4 12. e-4 x e –2 13. f-7 x f-5 14. g2 x g3 x g-5 • a3 x a4 • b4 x b3 • c2 x c 5 • d5 x d7 • e4 x e-3 • f -5 x f4 • g -4 x g-2

  6. Rydym yn gallu gwneud yr un peth gyda rhifau Enghraifft 23 x 22 = 2 x 2 x 2x 2 x 2 = 25 Ymarfer 5. 64 x 67 x 65 6. 77 x 73 x 73 7. 89 x 84 x 8-2 8. 9-7 x 94 1. 23 x 24 2. 34 x 33 3. 42 x 4 5 4. 55 x 57

  7. Rheol 2: Rhannu Indecsau RHEOLAU INDECSAU Ystyriwn a5 ÷ a2 a x a x a x a x a a x a = a x a x a = a3 Y rheol gyffredinol: am ÷ an = am - n

  8. Ymarfer • 8. 210 ÷ 24 • 9. 34 ÷ 33 • 10. 47 ÷ 4 • 53 ÷ 5-2 • 64 ÷ 67 • 13. 77 ÷ 73 • 14. 89 ÷ 84 • a6 ÷ a4 • b8 ÷ b3 • c7 ÷ c 3 • d5 ÷ d7 • e4 ÷ e-3 • f -5 ÷ f4 • g -4 ÷ g-2

  9. RHEOLAU INDECSAU Rheol 3: Codi Indecs i bŵer arall Ystyriwn (a2 ) 3 Mae hwn yn golygu a2 x a2 x a2 = a6 Y rheol gyffredinol: (am)n = am x n

  10. Ymarfer • 8. (210)4 • 9. (34)3 • 10. (47)2 • (53)-2 • (64)7 • 13. (77)3 • 14. (89)-4 • (a6)4 • (b8)3 • (c7)3 • (d5)7 • (e4)-3 • (f -5)4 • (g -4)-2

  11. RHEOLAU INDECSAU Rheol 4: Indecsau Negatif Gwyddwn fod a2 ÷ a5 = a-3 ond hefyd gallwn ystyried y broblem mewn ffurf mwy syml: a2 ÷ a5 = a x a = 1 = 1 a x a x a x a x a a x a x a a3 Felly mae a -3 = 1 a3 a-n = 1 an Y rheol gyffredinol:

  12. RHEOLAU INDECSAU Rheol 5: Indecsau Israddau Mae angen darganfod pa bŵer sy’n cynrychioli’r arwydd √. Ystyriwn bod rhaid i a* x a* = a, ac felly a *+ * = a Os yw * + * = 1. rhaid bod * = ½ Felly, √a = a1/2 Y rheolau cyffredinol: na = a1/n ac n(am) = am/n = (na)m Enghreifftiau a = a1/2 4a = a1/4 5a = a1/5

  13. RHEOLAU INDECSAU Rheol 6: Indecsau 0 a 1 a0 = 1 Y rheolau cyffredinol: a1 = a Enghreifftiau 60 = 1g1 = g14760 = 1

  14. Enghreifftiau symleiddio (6f4 x 4f2 ) ÷ 2f5 = 24f6 ÷ 2f5 = 12f (4g7 ÷ 2g-3) x 5g-6 = 2g10 x 5g-6 = 10g4 [(a5/2 x a-1/2) ÷ a-2]3/2 = [a2 ÷ a-2]3/2 = [a4]3/2 = a6

  15. Ymarfer • Symleiddiwch: • (82)-1 11. 2a2 x 3a6 • (53) 0 12. 8a6 ÷ 2a4 • 321/5 13. 4x14 ÷ 2x -2 • 4. 91/2 14. (2f2 x 6f5 ) ÷ 3f3 • 5. 16 15. (24g8 ÷ 3g-5 ) x 2g-3 • 6. 2-3 16. (a3 x a2)÷ a-4 • 7. 820 17. 811/4 • 8. 251/2 18. -641/3 • 9. 4 16 19. 3 -3 • 10. 81/3 20. 125-1/3

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