Algebraic Operations Adding / Sub Indices Negative Indices Fraction Indices Harder Indices

Starter Questions 1.Simplify the following fractions :

Learning Intention Success Criteria 1.To explain how to multiply and divide indices by adding / subtracting powers. 1.Understand basic rules for indices. Algebraic Operations 2.Simplify indices.

Indices a n is a short hand way of writing a x a x a ……. (n factors) a is called the base number and n is called the index number Calculate :2 3 x 2 2 x 2 x 2 2 x 2 x 2= 32 Calculate :2 5 = 32 Can you spot the connection !

Indices Calculate :4 3 ÷ 4 2 ÷ 4 x 4 4 x 4 x 4= 4 Calculate :4 1 = 4 Can you spot the connection ! a m x a n = a (m + n) simply add powers a m ÷ a n = a (m - n) simply subtract powers

What Goes In The Box ? b 3 x b 5 = y 9 ÷ y 5 = f 4 x g 5 = a 3 x a 0 = b8b8 y4y4 Exercise 11 Page 209

Starter Questions 1.Simplify the following fractions :

Learning Intention Success Criteria 1.To explain how to handle fractional indices of powers. 1.Understand basic rules for fractional indices. Algebraic Operations 2.Simplify fractional indices.

More Rules By the division rule Fractions as Indices

More Rules Fractions as Indices

More Rules Fractions as Indices

Ex. 12 Page 210

Starter Questions 1.Rationalise the denominator :

Learning Intention Success Criteria 1.To explain how to handle fractional indices of powers. 1.Understand basic rules for fractional indices. Algebraic Operations 2.Simplify fractional indices.

Fractions as Indices

In general we have

Fractions as Indices Examples : Simplify the following

Fractions as Indices Final Rule

Fractions as Indices Examples

Fractions as Indices Examples

Fractions as Indices Example :Change to index form Example :Change to surd form

Fractions as Indices Exercise 13 Page 211