# Algebraic Manipulation: Laws of Indices and Flip Root Power Method

Dr. J Frost's chapter 1 covers basic laws of indices, including expanding and simplifying expressions. The flip root power method is also discussed with multiple examples.

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1. C1: Chapter 1 Algebraic Manipulation Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 2 nd September 2013

2. Starter Expand the following. ? ? ? ? ?

3. Recap: Basic Laws of Indices ? ? ? ? ? ? ? ?

6. Textbook Fail Example 7d on page 9 is wrong: ? Whenever you have fractional powers where the denominator is even, by DEFINITION, you only consider the positive solution.

7. Exercises 1 2 3 4 5 6 7 8 9 Simplify: Evaluate: 10 11 12 13 14 15 16 17 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

9.

11. Exercises 1 2 3 5 Simplify: ? ? ? ? 6 ? ? 7 9 10 11 Evaluate: 12 8 ? ? ? ? ? ?

13. Factorising SKILL 1 Taking out a single factor SKILL 3 Difference of two squares (Use commando method or splitting the middle term method) ? ? ? ? ? ? ? ? ? ? ?

14. Exercises Page 7 Exercise 1E Evens Page 9 Exercise 1F 1g,h,i , 2

15.

16. ? ? And thats it! Laws of Surds

17. Using these laws, simplify the following: ? ? ? ? ? Laws of Surds

18. ? ? ? Work these out with neighbour. Simplify as much as possible. Well feed back in a few minutes. ? Expansion involving Surds ?

19. Its convention that the number inside the surd is as small as possible, or the expression as simple as possible. This sometimes helps us to further manipulate larger expressions. ? ? ? ? Simplifying Surds

20. This sometimes helps us to further manipulate larger expressions. ? ? ? Simplifying Surds

21. Heres a surd. What could we multiply it by such that its no longer an irrational number? ? ? Rationalising Denominators

22. In this fraction, the denominator is irrational. Rationalising the denominator means making the denominator a rational number. What could we multiply this fraction by to both rationalise the denominator, but leave the value of the fraction unchanged? ? ? Theres two reasons why we might want to do this: 1. For aesthetic reasons, it makes more sense to say half of root 2 rather than one root two-th of 1. Its nice to divide by something whole! 2. It makes it easier for us to add expressions involving surds. Rationalising Denominators

23. ? ? ? Rationalising Denominators

24. ? ? Rationalising Denominators

26. Rationalise the denominator. Think what we need to multiply the fraction by, without changing the value of the fraction. ? ? Rationalising Denominators

27. Rationalise the denominator. Think what we need to multiply the fraction by, without changing the value of the fraction. ? ? Rationalising Denominators

28. Exercises Page 12 Exercise 1H Odds