1 / 20

Lesson 2- Laws of Indices

Lesson 2- Laws of Indices. Objectives To know what indices are To learn the rules of indices. What are Indices?. Indices provide a way of writing numbers in a more compact and convenient form Indices is the plural of Index An Index is often referred to as a power. For example. = 5 3.

todd
Download Presentation

Lesson 2- Laws of Indices

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lesson 2- Laws of Indices • Objectives • To know what indices are • To learn the rules of indices INTO Foundation L2

  2. What are Indices? • Indices provide a way of writing numbers in a more compact and convenient form • Indices is the plural of Index • An Index is often referred to as a power INTO Foundation L2

  3. For example = 53 5 x 5 x 5 2 x 2 x 2 x 2 = 24 75 7 x 7 x 7x 7 x 7 = 75 5 is the INDEX or POWER 7 is the BASE NUMBER 75 & 24 are numbers in INDEX FORM INTO Foundation L2

  4. 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 combine BASE NUMBERS if they are the same INTO Foundation L2

  5. Rule 1 : Multiplication 26 x 24 = 210 24 x 22 = 26 35 x 37 = 312 General Rule Law 1 am x an = am+n INTO Foundation L2

  6. Rule 2 : Division 26÷ 24 = 22 25÷ 22 = 23 35÷ 37 = 3-2 General Rule Law 2 am÷ an = am-n INTO Foundation L2

  7. Rule 3 : Brackets (26)2 = 26 x 26 = 212 (35)3 = 35 x 35 x 35 = 315 General Rule Law 3 (am)n = am x n INTO Foundation L2

  8. Rule 4 : Index of 0 How could you get an answer of 30 ? 35÷ 35 = 35-5 = 30 30 = 1 General Rule Law 4 a0 = 1 INTO Foundation L2

  9. Putting them together? 26 x 24 23 = 210 23 = 27 35 x 37 34 = 312 34 = 38 25 x 23 24 x 22 = 28 26 = 22 INTO Foundation L2

  10. Works with algebra too! 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 INTO Foundation L2

  11. ..and a mixture… 2a3 x 3a4 = 2 x 3 x a3 x a4 = 6a7 8a6÷ 4a4 = (8 ÷ 4) x (a6 ÷ a4) = 2a2 2 2 8a6 4a4 = 2a2 INTO Foundation L2

  12. Fractional indices • (Using Law 1) We could write But So INTO Foundation L2

  13. Fractional Indices • Similarly General Rule Law 5 INTO Foundation L2

  14. Negative Index Numbers. Simplify the expression below: To understand this result fully consider the following: 5 3 5 7 = 5 - 4 Write the original expression again as a quotient: Expand the numerator and the denominator: Cancel out as many fives as possible: Write as a power of five: Now compare the two results: INTO Foundation L2

  15. Negative Indices • The last Index rule am General Rule Law 6 a-m = 1 INTO Foundation L2

  16. Summary Rule 1 : Multiplication of Indices. a n x a m =……… Rule 2 : Division of Indices. a n  a m = ……. Rule 4 : For Powers Of Index Numbers. ( a m ) n = ….. Rule 6 : For negative indices a - m =……. Rule 3 : For Powers Of Index Numbers. a 0 = ….. Rule 5 : For fractional indices a1/n = n√a INTO Foundation L2

  17. Exercises • Section 2- Working with Indices • Additional Questions if you get that far! INTO Foundation L2

  18. Travelling to Mars How long would it take a space ship travelling at an average speed of 2.6 × 103 km/h to reach Mars 8.32 × 107 km away? INTO Foundation L2

  19. Calculations involving standard form Rearrange to give distance speed = time distance time = speed 8.32 × 107 Time to reach Mars = 2.6 × 103 How long would it take a space ship travelling at an average speed of 2.6 × 103 km/h to reach Mars 8.32 × 107 km away? = 3.2 × 104 hours This is 8.32 ÷ 2.6 This is 107÷ 103 INTO Foundation L2

  20. Calculations involving standard form 3 2 4 . EXP Use your calculator to work out how long 3.2 × 104 hours is in years. You can enter 3.2 × 104 into your calculator using the EXP key: Divide by 24 to give the equivalent number of days. Divide by 365 to give the equivalent number of years. 3.2 × 104 hours is over 3½ years. INTO Foundation L2

More Related