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I.PowersDefinition : When a number is to be multiplied by itself repeatedly, the result is a power

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Texte intégral

(1)

de

AND

n

n

b1n

n

n

n

1

2x2

2

3

23

8

n

n

2

2

2

a)

2x23x43x –4x25

b)

2x38x26x – x25x –3

3x36x

4x2–2

x2

5x

Vocabulary:

base – coefficient – constant – to cube – exponent – expression – index (indices) – multiplicative inverse – like (signs / terms) – opposite – ((to raise) to the) power (of) – reciprocal – to square – term – unknown – unlike (signs / terms) – variable

2014/15 - 2de - Worksheet #2-0a-3 POWERS and BASIC ALGEBRA page 1/4

(2)

2

–7x – 5 Remove brackets Factorising:

6x27x –5 = 3x –52x1

Put in brackets If possible, factorise also the constants. Example:

3 p212p12 = 3p24p4 = 3p –22

2

2

2

2

2

2

2

2

3

3

2

2

3

3

3

2

2

3

3

3

2

2

3

3

2

2

2

2

2

2

4x –

4x –2x

2x –2

2x

3x2

6x

2

3

2x2

8x –4

2

2

6x y3y2

5x220y2

x

2y

2

x24y2

ac –2bd – a d

2b c

x2−9

4x2−9

3625x2

81x2 1

16

Vocabulary: brackets – difference of two squares – to expand – to factorise – special factor – special expansion – to take out

2014/15 - 2de - Worksheet #2-0a-3 POWERS and BASIC ALGEBRA page 2/4

(3)

A

x2

y2

A

2

2

1

2

4

1

5

n

p

np

2c2d

3c3d2

2

3

6

2

3

32

5

2

12

3

2

3

2

5

3

3a2

4a3

2x2y

3x y

2a2b2

5b2

6x3

4x3y3

2x2

3x4

2

2

n

p

n−p

n

p

n−p

n

p

pn

32

3−2

1

2

3

32

1

6s7t

12s3t2

7

3

73

4

2

2−1

7

3

2

4

Vocabulary: to evaluate – to substitute ... for ...

2014/15 - 2de - Worksheet #2-0a-3 POWERS and BASIC ALGEBRA page 3/4

(4)

2

4

3

5

5

3

5

3

5

8

5

3

4

7

2

3

3

3

4

4

2

−3

8

5

n

n

n

: to raise a product to a power, raise every factor to the power example : Work out

A = 7×112×115×72

2

2

5

2

2

2

2

5

22

25

4

7

 ab 

n

nn

2

4

2

2

4

4

A = 72×114

112×74

A = 112

72

n

p

n p

3

2

2

2

3

3

3

3

3

3

3

2

2

2

2

4

2

2

2

4

2

2

2

2

2

3

3

4

4

2

2

3

4

3

2

4

2

2

5

4

2

4

2

4

3

2

D=

3433

3×74

212

2×

1711



5

2014/15 - 2de - Worksheet #2-0a-3 POWERS and BASIC ALGEBRA page 4/4

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