Negatieve getallen en machten
Uitleg
2H03.6 Uitleg ....................................................................................................................................
Bestudeer uit de kennisbank het onderdeel
negatieve getallen en machten
Bekijk ook het volgende filmpje: 
Maak daarna de opgaven.
Opgaven
2H03.6 Opgaven .........................................................................................................
| 1 |
|
Alles zonder rekenmachine! |
Neem over en vul in:
| (-3)2 = ... × ... = ... |
-32 = ... × ... = ... |
| (-3)3 = ... × ... × ... = ... |
-33 = ... × ... × ... = ... |
| 2 |
|
Alles zonder rekenmachine! |
Bereken de volgende machten. Schrijf tussenstappen op!
| (-2)3 = ...... = ... |
-23 = ...... = ... |
| (-4)2 = ...... = ... |
-42 = ...... = ... |
| (-5)4 = ...... = ... |
-54 = ...... = ... |
| 5-2 = ...... = ... |
(-3)0 = ... |
| 3 |
|
Alles zonder rekenmachine! |
Bereken. Schrijf ook de tussenstappen op!
| (4 + 2)2 + 32 |
(42 - 19)3 - 42 |
| 4 + 23 : 4 |
-22 × -32 : 6 |
| \(\small{ \mathsf{ -6\ +3^2- \sqrt{5^2 - 3^2} } }\) |
\(\small{ \mathsf{ -\sqrt{13^2 - 12^2}-3^3 } }\) |
| \(\small{ \mathsf{ ( \sqrt{5^2 - 3^2})^3:8-7 } }\) |
\(\small{ \mathsf{ - \sqrt{11+(-3)^2+5} } }\) |
Bereken.
| (52 -32)3 : 82 - 72 |
92 + 8 × 9 : 18 |
| (63 + 3) - 42 |
33 : 3 + 2 × (10 - 12)2 |
| 5 × -32 + (22 + 5)2 |
19 + (-5)3 + 132 - 73 |
| 5-2 × 103 : 8 + 92 |
-42 × 2-3 + 42 × -23 |
Uitwerkingen
2H03.6 Uitwerkingen ..........................................................................................................
| (-3)2 = -3 × -3 = 9 |
-32 = - 3 × 3 = -9 |
| (-3)3 = -3 × -3 × -3 = -27 |
-33 = - 3 × 3 × 3 = -27 |
| (-2)3 = -2 × -2 × -2 = -8 |
-23 = -2 × 2 × 2 = -8 |
| (-4)2 = -4 × -4 = 16 |
-42 = -4 × 4 = -16 |
| (-5)4 = -5 × -5 × -5 × -5 = 625 |
-54 = -5 × 5 × 5 × 5 = -625 |
| 5-2 = \(\color{ red} {\mathsf{ \small{ 1 \over 5^2} } } \) = \(\color{ red} {\mathsf{ \small{ 1 \over 25} } }\) |
(-3)0 = 1 |
|
(4 + 2)2 + 32 =
62 + 9 =
36 + 9 = 45
|
(42 - 19)3 - 42 =
(16 - 19)3 - 16 =
(-3)3 - 16 =
-27 - 16 = -43
|
|
4 + 23 : 4 =
4 + 8 : 4 =
4 + 2 = 6
|
-22 × -32 : 6 =
-4 × -9 : 6 =
36 : 6 = 6
|
|
\(\small{ \mathsf{ -6\ +3^2- \sqrt{5^2 - 3^2} } }\)
\(\color{red}{\small{ \mathsf{ -6\ +9- \sqrt{25 - 9} } }}\)
\(\color{red}{\small{ \mathsf{ -6\ +9- \sqrt{16} } }}\)
\(\color{red}{\small{ \mathsf{ -6\ +9-5 } } }\) = \(\color{red}{\small{ \mathsf{ -2 } }}\)
|
\(\small{ \mathsf{ -\sqrt{13^2 - 12^2}-3^3 } }\)
\(\color{red}{ \small{ \mathsf{ -\sqrt{169 - 144}-27 } } }\)
\(\color{red}{ \small{ \mathsf{ -\sqrt{25}-27 } } }\)
\(\color{red}{ \small{ \mathsf{ -5-27 } } }\) = \(\color{red}{ \small{ \mathsf{ -32 } } }\)
|
|
\(\small{ \mathsf{ ( \sqrt{5^2 - 3^2})^3:8-7 } }\) =
\(\color{red}{ \small{ \mathsf{ ( \sqrt{25 - 9})^3:8-7 } } }\) =
\(\color{red}{ \small{ \mathsf{ ( \sqrt{16})^3:8-7 } } }\) =
\(\color{red}{ \small{ \mathsf{ (4)^3:8-7 } } }\) =
\(\color{red}{ \small{ \mathsf{ 64:8-7 } } }\) =
\(\color{red}{ \small{ \mathsf{ 8-7 } } }\) = \(\color{red}{ \small{ \mathsf{ 1 } } }\)
|
\(\small{ \mathsf{ - \sqrt{11+(-3)^2+5} } }\) =
\(\color{red}{ \small{ \mathsf{ - \sqrt{11+ 9 +5} } } }\) =
\(\color{red}{ \small{ \mathsf{ - \sqrt{25} } } }\)= \(\color{red}{ \small{ \mathsf{ - 5 } } }\)
|
| (52 -32)3 : 82 - 72 = 15 |
92 + 8 × 9 : 18 = 85 |
| (63 + 3) - 42 = 203 |
33 : 3 + 2 × (10 - 12)2 = 17 |
| 5 × -32 + (22 + 5)2 = 36 |
19 + (-5)3 + 132 - 73 = -280 |
| 5-2 × 103 : 8 + 92 = 86 |
-42 × 2-3 + 42 × -23 = -130 |
