index laws miss hudson’s maths. indices 2525 base value power (indice) miss hudson’s maths

Index Laws

Miss Hudson’s Maths

Indices

25

Base Value

Power (Indice)

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When multiplying terms with the same base we add the powers.

Eg 1: y3 x y4 = y7

Eg 2: 23 x 25 = 28

Eg 3: 3 m2 x 2 m3 = 6 m5

1st Index Law: Multiplication

Eg 4: c2d5 x 6c5d = 6 c7d6

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98 ÷ 95 =

2nd Index Law: Division

9 x 9 x 9 x 9 x 9 x 9 x 9 x 9

9 x 9 x 9 x 9 x 9= 93

So although it has a divide sign, when we are dividing indices we actually subtract them.However this can only be done when there is the same base!

Miss Hudson’s Maths

When dividing terms with the same base we subtract the powers.

eg 1: p 8 ÷ p 2 = 2p

p8p 6

eg 2: 20x7 ÷ 4x3 3

7

4

20

x

x

1

5 5 x4

eg 3: 415

10

m

m52

3 32 m or 3

2m

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You must multiply the powers together, remembering

Multiply everything inside the brackets individually.

(x2)4 = x8

(5b3)2 =25b6

(-3y)2 =9y2

(-2n4)3 =-8n12

3rd Index Law: Power to a further power.

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4th Index Law: Power of zero

Any term to the power of 0, always equals 1.

d0 = 1

50 = 1

40 x 6 = 1 x 6 = 6

132 ÷ 132 = 130 = 1

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h2 x h3 =h5

-3 x 4y =

-12y

2w x 5w2 =

10w3

4b3 x -2b4 =-8b7

(x2)4 =x8

(5b3)2 =25b6

(-3y)2 =9y2

(-2n4)3 =-8n12

Mental Maths:

3

5

a

aa 2

a

a

2

2

2

a

2

5

3

6

x

x2x 3

3

5

15

12

h

h

5

4 2h

5

2

2

6

t

t3

3

t

x

x 4)3( 81x 3

27

32

20

16

nm

nm55

4

m

n

d0 = 1a5

8z0 x 5z5 =

40z5

52 x 5 x 50 =

53

S0 x 42 x s0 =

42

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(3x4)3

= (3x4) x (3x4) x (3x4)= 3 x 3 x 3 x 4 x 4 x 4 = 33 x 43

(Using the first index law)

5th Index Law: Removing Brackets (Products)

You must remember that if there is a letter or number by itself, it is to the power of 1.

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6th Index Law: Removing Brackets (quotient)

x x x x x

=

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Revision 25 = 2 x 2 x 2 x 2 x 2 = 32

Operation Rule Example

Multiplying Add powers y5 x y4 = y9

Dividing Subtract powers

Powers of Powers

Multiply powers

Powers of zero Always = 1 ao = 1

Four rules for working with powers

25powerindex orexponent

base

25

7

aa

a

1243 xx

Same base

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Remember that:

am x an = am+n eg y3 x y 4 = y7

eg

(am)n = amn eg (y 2)3 = y 6

(ab)m = ambm eg (2y)4 = 16y4

nmn

m

aa

a

These rules work the same if the base is a number eg: 23 x 22

=25

5

7

4

442

(32)4 = 38

42

6

yy

y

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7th Index Law: Negative Indices

6-2 =

34 ÷ 39 =

=

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8th Index Law: Fractional Indices

= √36

=

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Important numbers to remember:2 = 21

4 = 22

8 = 23

16 = 24

32 = 25

64 = 26

128 =

27

256 =

28

512 =

29

3 = 31

9 = 32

27 = 33

81 = 34

243 =

35

5 = 51

25 = 52

125 = 53

625 = 54

3125 =

55

Miss Hudson’s Maths