Rekenregels voor machten
1

16

27

1000

25

32

0

7

1

0,25

1

8

25

2

2 9

3 8

6 7

7 5

5 9

10 15

x 5

y 11

z 6

3

3 6

5 2

10 4

x 5

y

1

x 5

y 2

z 10

4

5 6

3 10

2 15

7 20

8 21

10 24

x 16

y 3

z 25

5

9 25

27 64

1 32

6

x 4 81

x 3 y 3

y 2 16

32 k 5

7

x 7 y 7

32 x 5

9 x 2

a 4 b 4 c 4

8

64 27

y 8

y 7 x 4

Rekenen met negatieve exponenten
9
a

2000 ; 4000 ; 32.000

b

1000 2 t

c

B = 1000 2 t

d

500 ; 250 ; 125 .

e

1000 2 1 = 500 ; 1000 2 2 = 250 ; 1000 2 3 = 125

f

1000 2 5 = 31,25 ; 1000 2 5 = 31,25

g

1000 2 5 = 1000 2 5 dus (deel linker- en rechterlid door 1000 ): 1 2 5 = 2 5

10

3 3 = 1 3 3 = 1 27

5 2 = 1 5 2 = 1 25

2 6 = 1 2 6 = 1 64

10 4 = 1 10 4 = 1 10 000

( 1 2 ) 1 = 1 1 2 = 2

( 1 5 ) 2 = ( 5 1 ) 2 = 5 1 2 = 5 2 = 25

( 2 1 2 ) 1 = 1 2 1 2 = 2 5

( 2 3 ) 2 = 1 ( 2 3 ) 2 = 1 4 9 = 9 4 = 2 1 4

11

( x 2 ) 3 ( x 4 ) 2 = x 6 x 8 = x 2

( x x 2 x 3 ) 4 = ( x 6 ) 4 = x 24

( x 2 ) 3 x 1 = x 6 x 1 = x 7

( 4 x ) 3 3 x 2 = 4 3 x 3 3 x 2 = 192 x

12

( 2 x ) 3 3 x 2 = 2 3 x 3 3 x 2 = 24 x 1 = 24 x

( x 2 ) 3 4 x 5 = x 6 4 x 5 = 4 x 1

7 x 1 ( x 3 ) 2 = 7 x 1 x 6 = 7 x 7

5 x 4 4 x 5 = 5 4 x 4 x 5 = 5 4 x 4 5 = 5 4 x 1 = 1 1 4 x

( 3 x 2 ) 3 ( 2 x 3 ) 2 = 3 3 ( x 2 ) 3 2 2 ( x 3 ) 2 = 27 x 6 4 x 6 = 27 4 = 6 3 4

( 2 x 3 ) 4 x 3 x 5 = 2 4 ( x 3 ) 4 x 2 = 16 x 12 x 2 = 16 x 10

13

3,412 10 3

5,217 10 1

8,21 10 5

1,03 10 4

2,3 10 2

9,35 10 4

7,5 10 7

8,3 10 10

Rekenen met wortels
14

2

6

12

20

60

120

0,2

0,6

1,2

15
a

4 25 = 100

b

9 16 = 9 16

c

a b = a b

d

4 9 = 4 9

e

25 36 = 25 36

f

a b = a b

16

70

110

300

2 3

5 6

1 3 10

2 1 2

1 3 5

1 3 4

17

3 x

8 y

12 z

x 4

y 7

z 10

6 x

9 y

8 z

18

4,80 x

11,62 y

3,88 z

0,41 x

0,76 y

1,11 z

4,52 a

5,02 b

3,31 c