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Mastering Rules for Indices: A Comprehensive Guide

Understand and apply the rules of indices with this comprehensive starter guide. Learn how to multiply, divide, simplify powers, work with brackets, and more. Test your knowledge with a quick recap and challenging exercises.

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Mastering Rules for Indices: A Comprehensive Guide

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  1. Rules for Indices Understanding the rules for indices Applying the rules of indices

  2. Starter Copy and complete the following filling in the missing words by using the words in the box below: To multiply numbers with indices we ______ the powers. As a formula this can be written as ______. To divide numbers with indices we ______ the powers. As a formula this can be written as ______. It is not possible to simplify powers if they have different ______. I need to be especially careful when there are ______ numbers involved. bases add am÷ an = am - n subtract am × an = am + nnegative

  3. Quick Recap! x6 × x4 x3 × x-2 3x × 2x2 5y-2 × 4y-2 y8 ÷ y4 y-4 ÷ y5 4y6 ÷ 2y3 9x-3 ÷ 3y-2 8y6 ÷ 8y6 Use your knowledge of laws of indices to simply the following

  4. Special Rule x0 = 1 Anything to the power of 0… 80 = 1 = 1 30 = 1 (monkey)0 = 1 What happens when you get x0? (xy)0 = 1 20000 = 1

  5. Brackets - A power to a power When we have a question involving brackets, we MULTIPLY the indices. Can you work out why using this example: (x4)2 = x8 What should we do if we have (2b3)3? How could you write this rule using algebra?

  6. Brackets – A power to a power Try these questions: (f 6)2 (h3)4 (e5)2 (k3)-4 (y2)-4 (x-3)-5 (d-4)-6 [(y3)-2]5 Now try these harder questions: (2t2)3 (3y2)2 (6m7)2 (2z-3)4 (3t4)3 (3x2y4)3 (4c-2d6)3 (5e4f6g-4)3 For a question involving brackets multiply the indices

  7. How much have you learnt? y6× 2y 3x2 × 4y4 y ÷ 3y2 2x2y-4 × 5xy6 (3x3y)2 25x-2y3 ÷ 5x4y-2 40 20x4 ÷ 20y4 Can you cope answering mixed questions? Don’t forget the monkey!!!

  8. Plenary Spot the odd one out timed quiz (part 2) Just because you were so bad at it last time……

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