Indices Squares and square roots Cubes and cube

Indices Squares and square roots Cubes and cube roots Index form

Use positive integer indices to write repeated multiplication calculations, for example 2 x 2 x 2 = 24. Calculate positive integer powers and for example 2 to the power 4 is 16. Recognise simple powers of 2, 3, 4 and 5. E. g. 9 = 32 a x a = a 3 a 2 x a 3 = a 5

1

2 1 1 x 2 1 21 20

4 2 1 1 x 2 x 2 1 22 21 20

8 4 2 1 1 x 2 x 2 x 2 1 x 2 1 23 22 21 20

1 1

3 1 1 x 3 1 31 30

9 3 1 1 x 3 x 3 1 32 31 30

27 9 3 1 1 x 3 x 3 x 3 1 x 3 1 33 32 31 30

1 1

4 1 1 x 4 1 41 40

16 4 1 1 x 4 x 4 1 42 41 40

64 16 4 1 1 x 4 x 4 x 4 1 x 4 1 43 42 41 40

1 1

10 1 1 x 10 1 100

100 10 1 1 x 10 1 102 101 100

1000 10 1 1 x 10 x 10 1 x 10 1 103 102 101 100

1 1

x 1 1. x 1 x 0

x 2 x 1 1. x. x 1 x 2 x 1 x 0

x 3 x 2 x 1 1. x. x. x 1 x 3 x 2 x 1 x 0

x 2 x x 2 3 25 x x 2 8 100 x x 2 4 49 x

8 x x 2 1000 x x 2 27 x 2 x 64 x 2 x 125 x 2 x

x 3 x 3 x 25 x 3 x 100 36 x x 3 9 x 4 x x 3 49 x

12 = 22 = 32 = 42 = 52 = 62 = 102 =

13 = 23 = 33 = 43 = 53 = 63 = 103 =

? 1 7

x+1=7 ? 1 7

x+1=7 x=6 6 1 7

x+2=7 ? 7

x+2=7 x=5 5 7

2 x + 1 = 7 3 3 7 x=3

25 10 ?

x 2 + 1 = 10 25 10 ?

x 2 = 9 25 9 10 ? 1

x 2 = 9 25 9 10 3 1 x=3

? 30

x 2 + x = 30 ? 30

5 25 30 5 x=5

Base 2 Index Form 8 4 2 1 1 x 2 x 2 x 2 1 x 2 1 23 22 21 20

Base 2 Index Form 1 x 2 x 2 x 2 x 2 27 1 x 2 x 2 x 2 1 x 2 x 2 26 25 24 8 4 2 1 1 x 2 x 2 x 2 1 x 2 1 23 22 21 20

Base 3 Index Form 27 9 3 1 1 x 3 x 3 x 3 1 x 3 1 33 32 31 30

Base 3 Index Form 27 1 x 3 x 3 x 3 x x 3 x 3 3 37 36 9 3 1 1 x 3 x 3 x 3 1 x 3 x 3 1 35 34 33 32 31 30

Index Form 63 = 1 x 6 x 6 x 6 = 216 43 = 1 x 4 x 4 x 4 = 64 74 = 1 x 7 x 7 85 = 1 x 8 x 8 x 8 106 = 1 x 10 x 10 x 10 x 10 a 7 = 1 xaxaxaxa a 4 = 1 xaxa

True or False a 2 x a 3 = a 6 a 2 x a 3 = 2 a 6 a 2 a 5 a 2 x a 3 = 2 a 5 5 a a 2 x a 3 = 6 a a 2 x a 3 =