Überblick Negative Zahlen/Wiederholung Potenzen: Unterschied zwischen den Versionen

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Markierung: 2017-Quelltext-Bearbeitung
Keine Bearbeitungszusammenfassung
Markierung: 2017-Quelltext-Bearbeitung
Zeile 36: Zeile 36:
* (-13)⋅ (-13) ⋅ (-13)  
* (-13)⋅ (-13) ⋅ (-13)  
* (-88) ⋅ (-88) ⋅ (-88) ⋅ (-88)  
* (-88) ⋅ (-88) ⋅ (-88) ⋅ (-88)  
{{Lösung versteckt|1
{{Lösung versteckt|1=
* (-3) ⋅ (-3) ⋅ (-3) ⋅ (-3) ⋅ (-3) = (-3)<sup>5</sup>
* (-3) ⋅ (-3) ⋅ (-3) ⋅ (-3) ⋅ (-3) = (-3)<sup>5</sup>
* (-13)⋅ (-13) ⋅ (-13) = (-13)<sup>3</sup>
* (-13)⋅ (-13) ⋅ (-13) = (-13)<sup>3</sup>
* (-88) ⋅ (-88) ⋅ (-88) ⋅ (-88) = (-88)<sup>4</sup>
* (-88) ⋅ (-88) ⋅ (-88) ⋅ (-88) = (-88)<sup>4</sup>
|2=Zum Nachlesen|3=Verbergen}}  
|2=Lösung|3=Verbergen}}  
|3=Üben}}
|3=Üben}}


Zeile 49: Zeile 49:
* (-5)<sup>3</sup>
* (-5)<sup>3</sup>
* (-10)<sup>5</sup>
* (-10)<sup>5</sup>
{{Lösung versteckt|1
{{Lösung versteckt|1=
* (-3) ⋅ (-3) ⋅ (-3) ⋅ (-3) = 81
* (-3) ⋅ (-3) ⋅ (-3) ⋅ (-3) = 81
* (-5)⋅ (-5) ⋅ (-5) = -125
* (-5)⋅ (-5) ⋅ (-5) = -125
* (-10) ⋅ (-10) ⋅ (-10) ⋅ (-10)⋅ (-10)= - 100 000
* (-10) ⋅ (-10) ⋅ (-10) ⋅ (-10)⋅ (-10)= - 100 000
|2=Zum Nachlesen|3=Verbergen}}  
|2=Lösung|3=Verbergen}}  
|3=Üben}}
|3=Üben}}

Version vom 14. Juni 2020, 16:40 Uhr


Überlegung

Weißt du noch was eine Potenz ist?
Versuche dir die Frage selbst zu beantworten.

Eine Potenz ist ein Produkt aus gleichen Faktoren. Dabei ist die Basis (oder auch Grundzahl) der mehrfach auftretende Faktor. Der Exponent (oder auch Hochzahl) gibt an, wie oft der gleiche Faktor vorkommt.

z.B. 45
4 ist die Basis und 5 der Exponent

45 = 4⋅4⋅4⋅4⋅4 = 1024


Übung 1

Berechne.

34 = 81()
23 = 8()
73= 343()
105 = 10000()


Info

Potenzen gibt es natürlich auch bei ganzen Zahlen.
(-2)3 = (-2) ⋅ (-2) ⋅ (-2) Das können wir in mehreren Schritten berechnen:
(-2)⋅(-2)⋅(-2)
= 4 ⋅(-2)

= -8


Übung 2

Schreibe als Potenz:

  • (-3) ⋅ (-3) ⋅ (-3) ⋅ (-3) ⋅ (-3)
  • (-13)⋅ (-13) ⋅ (-13)
  • (-88) ⋅ (-88) ⋅ (-88) ⋅ (-88)
  • (-3) ⋅ (-3) ⋅ (-3) ⋅ (-3) ⋅ (-3) = (-3)5
  • (-13)⋅ (-13) ⋅ (-13) = (-13)3
  • (-88) ⋅ (-88) ⋅ (-88) ⋅ (-88) = (-88)4


Übung 2

Schreibe als Produkt und berechne

  • (-3)4
  • (-5)3
  • (-10)5
  • (-3) ⋅ (-3) ⋅ (-3) ⋅ (-3) = 81
  • (-5)⋅ (-5) ⋅ (-5) = -125
  • (-10) ⋅ (-10) ⋅ (-10) ⋅ (-10)⋅ (-10)= - 100 000
Abgerufen von „https://rmgwiki.zum.de/index.php?title=Überblick_Negative_Zahlen/Wiederholung_Potenzen&oldid=16990“