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Unit 4: Mathematics

Unit 4: Mathematics. Aims Introduce the laws of indices. Objectives Identify the 4 laws of power. Use the laws of indices to calculate given formulas. A Look At Logarithms. Index & Base Exponential Series Transcendental Equations. Index & Base. What is an Index and what is a base?

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Unit 4: Mathematics

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  1. Unit 4: Mathematics Aims • Introduce the laws of indices. Objectives • Identify the 4 laws of power. • Use the laws of indices to calculate given formulas.

  2. A Look At Logarithms Index & Base Exponential Series Transcendental Equations

  3. Index & Base What is an Index and what is a base? 23 = 2 × 2 × 2 = 834 = 3 × 3 × 3 × 3 = 81 The 4 Laws of Indices am × an = a(m + n) am÷ an = a(m - n) (am)n = am × n n√am = am / n

  4. First law - Index Law for Multiplication = 53 5 x 5 x 5 = 24 2 x 2 x 2 x 2 = 75 7 x 7 x 7x 7 x 7 5 is the INDEX 7 is the BASE NUMBER

  5. Combining numbers x 2 x 2 x 2 x 2 5 x 5 x 5 = 53 x 24 We can not write this any more simply Can ONLY do that if BASE NUMBERS are the same

  6. First Law: Multiplication 26 x 24 = 210 24 x 22 = 26 35 x 37 = 312 General Rule am x an = am+n

  7. Second Law: Division 26÷ 24 = 32 25÷ 22 = 23 35÷ 37 = 3-2 General Rule am÷ an = am-n

  8. Third Law: Root √44 = 4(4 / 2) = 42 = 16 Dividing indices √16 × 25 =√16 ×√25 = 4 × 5 = 20 3√125 x 9 = 100.623

  9. 15.588 19.365 192 3√27 3√125/3 3√64²

  10. Perfect square 1 81 Ö1 = 1 Ö81 = 9 4 100 Ö4 = 2 Ö100 = 10 9 121 Ö9 = 3 Ö121 = 11 16 144 Ö16 = 4 Ö144 = 12 25 169 Ö25 = 5 Ö169 = 13 36 196 Ö36 = 6 Ö196 = 14 49 225 Ö49 = 7 Ö225 = 15 64 Ö64 = 8

  11. Fourth Law: Index Law for Powers (Brackets) (26)2 = 26 x 26 = 212 (35)3 = 35 x 35 x 35 = 315 General Rule (am)n = am x n

  12. Index Law for Powers

  13. Rule 4 : Index of 0 How could you get an answer of 30? 35÷ 35 = 35-5 = 30 General Rule a0 = 1 30 = 1

  14. 26 x 24 23 = 210 23 = 27 35 x 37 34 = 312 34 = 38 25 x 23 24 x 22 = 28 26 = 22

  15. a6 x a4 = a10 b5 x b7 = b12 c5 x c3 c4 = c8 c4 = c4 a5 x a3 a4 x a6 = a8 a10 = a-2

  16. 2a3 x 3a4 = 2 x 3 x a3 x a4 = 6a7 8a6÷ 4a4 = (8 ÷ 4) x (a6 ÷ a4) = 2a2 2 2 8a6 4a4

  17. = = = 2 = 2 = 2

  18. We know that: Listen Read phonetically This formula tells us that when a product is raised to a power, every factor of the product is raised to the power.This is the fifth index law and is known as the Index Law for Powers of Products.

  19. D³ C² X DC D²C² X DC • (g7h2k2a4)² X gk2 • g14h³k5a6gka2h

  20. C.

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