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Mastering Fractional Indices: Unlock the Power of Roots and Higher Power Operations

Learn all about fractional indices, roots, and higher power operations. Explore how to write and evaluate fractional indices, including square, cubic, and other roots. Understand handy powers and how to reverse any power to create roots. Practice with basic and more complex fractional indices to enhance your understanding.

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Mastering Fractional Indices: Unlock the Power of Roots and Higher Power Operations

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  1. Fractional Indices Oh Boy 

  2. What is to be learned? • What fractional indices are • How to write fractional indices as roots • How to evaluate fractional indices

  3. Other Roots Square Root √ √16 = 4 (because 42 = 16) Should really be written as 2√

  4. Cubic Root 23 = 8 33 = 27 43 = 64 53 = 125 so 3√64 = 4 3√1000 =10

  5. And There’s more!!!!!! We can make roots by reversing any power 24 = 16 so 4√16 = 2 (quartic root) 5√243? (quintic root- to be hereafter known as 5th root!) = 3

  6. Handy Powers – As well as squares 23 = 8 33 = 27 43 = 64 53 = 125 24 = 16 34= 81 44 = 256 54 = 625 25 = 32 35 = 243 Also 103 = 1000 104 = 10000 etc.

  7. What has this to do with indices? ½ 2√a same as a 3√a = a Rule p√a = a (root is number on the bottom!) 1/3 1/p

  8. ½ Ex 1 25 = 2√25 = 5 Ex 2. 125 = 3√125 = 5 1/3

  9. Fractional Indices - Basic • Indices that are fractions • The root is the number on the bottom Rule e√a = a 81 16 1/e ½ = 9 = 2√81 ¼ = 4√16 = 2 (because 24 = 16)

  10. You Try 1/3 ½ 1. 49 2. 27 3. 100 4. 16 5. 144 6. 64 7. 400 8. 10000 = 7 = 3 ½ ¼ = 10 = 2 1/3 ½ = 12 = 4 ¼ ½ = 20 = 10

  11. 3/2 What about a Root still on bottom Top number is power Ex1 25 =(2√25) = 5 = 125 3/2 3 3

  12. 5/3 Ex. 2 8 = (3√8) = 2 = 32 5 5

  13. Fractional Indices - Nastier • The root still on the bottom • Top number is the power. Rule (e√a )f= a f/e

  14. 3/2 16 = (2√16) = 4 = 64 3 3

  15. You Try 2/3 3/2 1. 162. 1000 3. 324. 49 5. 64 6. 81 Then p211 Q 1 = 100 = 64 4/5 3/2 = 16 = 343 2/3 ¾ = 16 = 27

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