Wiki-Quellcode von Lösung Potenzgesetze – Struktur statt Ergebnis
Version 3.1 von Martin Rathgeb am 2026/02/02 16:38
Verstecke letzte Bearbeiter
| author | version | line-number | content |
|---|---|---|---|
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1.1 | 1 | (%class=ml%) |
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2.1 | 2 | === ML zu a) === |
| 3 | Werte berechnen: | ||
| 4 | 1. {{formula}}2^3\cdot2^4=8\cdot16=128{{/formula}} | ||
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3.1 | 5 | 1. {{formula}}2^7=128{{/formula}} |
| 6 | 1. {{formula}}2^3\cdot3^3=8\cdot27=216{{/formula}} | ||
| 7 | 1. {{formula}}(2\cdot3)^3=6^3=216{{/formula}} | ||
| 8 | 1. {{formula}}2^4\cdot3^3=16\cdot27=432{{/formula}} | ||
| 9 | 1. {{formula}}3^3\cdot2^3=27\cdot8=216{{/formula}} | ||
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1.1 | 10 | |
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2.1 | 11 | Zuordnung: |
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3.1 | 12 | * {{formula}}(1)=(2){{/formula}} |
| 13 | * {{formula}}(3)=(4)=(6){{/formula}} | ||
| 14 | * {{formula}}(5){{/formula}} hat keinen Partner. | ||
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1.1 | 15 | |
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2.1 | 16 | === ML zu b) === |
| 17 | Begründung ohne Ausrechnen (Potenzen als Produkte gleicher Faktoren): | ||
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1.1 | 18 | |
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3.1 | 19 | * {{formula}}2^3\cdot2^4=(2\cdot2\cdot2)\cdot(2\cdot2\cdot2\cdot2)=2^7{{/formula}} |
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1.1 | 20 | |
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3.1 | 21 | * {{formula}}2^3\cdot3^3=(2\cdot2\cdot2)\cdot(3\cdot3\cdot3)=(2\cdot3)\cdot(2\cdot3)\cdot(2\cdot3)=(2\cdot3)^3{{/formula}} |
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1.1 | 22 | |
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3.1 | 23 | * {{formula}}2^3\cdot3^3=3^3\cdot2^3{{/formula}} (gleiche Faktoren, nur umgeordnet) |
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1.1 | 24 | |
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3.1 | 25 | * {{formula}}(2\cdot3)^3=(2\cdot3)\cdot(2\cdot3)\cdot(2\cdot3)=3^3\cdot2^3{{/formula}} |
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1.1 | 26 |