IndicesLearning objective:To understand the basic rules of indices - allTo investigate powers of 0 and 1 - mostTo investigate negative powers - someYou will require a scientific calculator and a pen.

Investigation

2²x 24 = = 2^

3 x 3³ = = 3^

5² x 5³ = = 5^

45 x 4² = = 4^

3³ x 33 = = 3^

4³÷ 4 = = 4^

2³÷ 2² = = 2^

3³÷ 3³ = = 3^

45 ÷ 4³ = = 4^

78 ÷ 7³ = = 7^

(2³)² = = 2^

Rules of indices

Multiplicationxa * x b

= x(a + b)

Divisionxa ÷ xb

= x(a-b)

Powers(xa)b

= x(ab)

Exercise

1) 3³ x 34 =

2) 7103 ÷ 7101 =

3) (8³)² =

4) (2³ ÷ 2²)5 =

Further investigation

What is x0?

What is x1?

Where x can be any number.What is the effect of negative powers?

Further investigation