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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
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