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Uitwerkingen! Hoofdstuk 3 Basisboek wiskunde Craats en Bosch
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Volledige uitwerkingen en antwoorden van het hoofdstuk 3 uit Basisboek wiskunde Jan Craats en Rob Bosch
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Clear elaboration!
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Hoofdstuk 3Machten en wortels
Schrijf alle volgende uitdrukkingen als een geheel getal of als een onvereenvoudigbare breuk.
3.1
A
23 = 2𝑥2𝑥2 = 8
B
32 = 3𝑥3 = 9
C
45 = 4𝑥4𝑥4𝑥4𝑥4 = 1024
D
54 = 5𝑥5𝑥5𝑥5 = 625
E
28 = 2𝑥2𝑥2𝑥2𝑥2𝑥2𝑥2𝑥2 = 256
3.2
A
(−2)3 = (−2)𝑥(−2)𝑥(−2) = −8
B
(−3)2 = (−3)𝑥(−3) = 9
C
(−4)5 = (−4)𝑥(−4)𝑥(−4)𝑥(−4)𝑥(−4) = −1024
D
(−5)4 = (−5)𝑥(−5)𝑥(−5)𝑥(−5) = 625
E
(−2)6 = (−2)𝑥(−2)𝑥(−2)𝑥(−2)𝑥(−2)𝑥(−2) = 64
Tip: - Wanneer de macht een even getal is wordt het antwoord positief
- Wanneer de macht een oneven getal is wordt het antwoord negatief
In de volgende sommen wordt de rekenregel: ‘delen door een breuk is vermenigvuldigen met het
omgekeerde’ toegepast. Zie uitleg en voorbeelden van deze rekenregel hoofdstuk 2.22
3.3
A
1 1 1
2−3 = 3 = =
2 2𝑥2𝑥2 8
B
1 1 1
4−2 = = =
42 4𝑥4 16
,C
1 1 1
3−4 = 4 = =
3 3𝑥3𝑥3𝑥3 81
D
1 1
7−1 = 1 =
7 7
E
1 1 1
2−7 = 7 = =
2 2𝑥2𝑥2𝑥2𝑥2𝑥2𝑥2 128
3.4
A
20 = 1
B
1 1
9−1 = 1 =
9 9
C
1 1 1
11−2 = 2 = =
11 11𝑥11 121
D
1 1 1
9−3 = 3 = =
9 9𝑥9𝑥9 729
E
1 1 1
10−4 = 4
= =
10 10𝑥10𝑥10𝑥10 10000
3.5
A
(−4)3 = (−4)𝑥(−4)𝑥(−4) = −64
B
1 1 1
3−5 = 5 = =
3 3𝑥3𝑥3𝑥3𝑥3 243
C
1 1 1 1
(−3)−3 = 3
= = =−
(−3) (−3)𝑥(−3)𝑥(−3) −27 27
D
24 = 2𝑥2𝑥2𝑥2 = 16
E
1 1 1
(−2)−4 = 4 = =
(−2) (−2)𝑥(−2)𝑥 (−2)𝑥(−2) 16
, 3.6
A
−20 = 1
B
02 = 0𝑥0 = 0
C
1 1
12−1 = 1 =
12 12
D
(−7)2 = (−7)𝑥(−7) = 49
E
1 1 1 1
(−2)−7 = 7 = = = −
(−2) (−2)𝑥(−2)𝑥 (−2)𝑥(−2)𝑥 (−2)𝑥(−2)𝑥 (−2) −128 128
3.7
A
2 2 22 2𝑥2 4
( ) = 2= =
3 3 3𝑥3 9
B
1 4 14 1𝑥1𝑥1𝑥1 1
( ) = 4= =
2 2 2𝑥2𝑥2𝑥2 16
C
4 3 43 4𝑥4𝑥4 64
( ) = 3= =
5 5 5𝑥5𝑥5 125
D
2 2 22 2𝑥2 4
( ) = 2= =
7 7 7𝑥7 49
3.8
A
2 −2 1 1 1 1 9 9
( ) = = 2= = = 1𝑥 =
3 2 2 2 2𝑥2 4 4 4
(3) 32 3𝑥3 9
B
1 −3 1 1 1 1 8 8
( ) = = 3= = = 1𝑥 = =8
2 1 3 1 1𝑥1𝑥1 1 1 1
(2) 23 2𝑥2𝑥2 8
C
7 −1 1 1 1 9 9
( ) = 1 = 1 = = 1𝑥 =
9 7 7 7 7 7
(9) 91 9
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