Wiki-Quellcode von Lösung Potenzgesetze – Struktur statt Ergebnis
Version 2.1 von Martin Rathgeb am 2026/02/02 16:32
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: | ||
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1.1 | 4 | (%class=abc%) |
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2.1 | 5 | 1. {{formula}}2^3\cdot2^4=8\cdot16=128{{/formula}} |
| 6 | 2. {{formula}}2^7=128{{/formula}} | ||
| 7 | 3. {{formula}}2^3\cdot3^3=8\cdot27=216{{/formula}} | ||
| 8 | 4. {{formula}}(2\cdot3)^3=6^3=216{{/formula}} | ||
| 9 | 5. {{formula}}2^4\cdot3^3=16\cdot27=432{{/formula}} | ||
| 10 | 6. {{formula}}3^3\cdot2^3=27\cdot8=216{{/formula}} | ||
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1.1 | 11 | |
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2.1 | 12 | Zuordnung: |
| 13 | - {{formula}}(1)=(2){{/formula}} | ||
| 14 | - {{formula}}(3)=(4)=(6){{/formula}} | ||
| 15 | - {{formula}}(5){{/formula}} hat keinen Partner. | ||
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1.1 | 16 | |
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2.1 | 17 | === ML zu b) === |
| 18 | Begründung ohne Ausrechnen (Potenzen als Produkte gleicher Faktoren): | ||
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1.1 | 19 | |
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2.1 | 20 | - {{formula}}2^3\cdot2^4=(2\cdot2\cdot2)\cdot(2\cdot2\cdot2\cdot2)=2^7{{/formula}} |
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1.1 | 21 | |
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2.1 | 22 | - {{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 | 23 | |
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2.1 | 24 | - {{formula}}2^3\cdot3^3=3^3\cdot2^3{{/formula}} (gleiche Faktoren, nur umgeordnet) |
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1.1 | 25 | |
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2.1 | 26 | - {{formula}}(2\cdot3)^3=(2\cdot3)\cdot(2\cdot3)\cdot(2\cdot3)=3^3\cdot2^3{{/formula}} |
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1.1 | 27 |