If a is a real number and n is a positive integer, then

1. If a is a real number and n is a positive integer, then = a.a.a.a … a (n times) index base The number a is called the base and n is called the index, and a nis read as ‘ a to the power of n ‘

2. Rules of Indices

3. Notes 1. 4. 2. 5. 3. 6.

4. Example 1 Evaluate each of the following without using calculator. (a) (b)

5. Example 2 Simplify each of the following. (a) (b) (c)

6. Example 3 Simplify in the form and

7. SURDS OBJECTIVES • Explain the meaning of a surd and its conjugate, and to carry out algebraic operations on surds • State the rules of indices

8. Surds Anirrational number and expressed in terms ofroot sign Positive integer Real number Note: a is not a perfect square, a > 0

9. Let’s pronounce correctly is nth root of a is square root of a is cube root of a is fourth root of a 9

10. Rules of surds

11. Algebraic Operations on Surds a) Multiplication When unlike surds are multiplied together, the product is a surd. Example 1: a) b)

12. b) Division Example 2: a) b)

13. c) Addition and Subtraction Example 3:

14. d) Expansion of Surds Expansion of Surds (Alternatively) :

15. Example 4:

16. Rationalising the Denominator The conjugate of the surd is

17. Example 5 : Rationalise the denominators of each of the following fractions.

18. Solving Equations Involving Surds Example 6: Solve the following equations. Give your answer in the set form.