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Kategorie: Matematika, 3) Matematická První Pomoc

Počítání s mocninami s přirozeným mocnitelem 2

Mocnina součinu, Mocnina podílu, Mocnina mocniny

4) Mocnina součinu

(3 . 4)3 = (3 . 4) . (3 . 4) . (3 . 4) = 33 . 43 Uvědom si, co znamená třetí mocnina - proto se v zápisu třikrát opakuje (3 . 4), pak už jen použiješ pravidlo pro násobení a sečteš mocnitele.

Při umocňování součinu umocníme každý činitel zvlášť.


Toto pravidlo se dá dobře použít v opačném směru, např. 25 . 55 = (2 . 5)5 = 105 = 100 000 .. nemusíme tedy nejprve určovat pátou mocninu dvou, pak pátou mocninu pěti a nakonec obě mocniny násobit. (Mimochodem by to bylo 32 . 3125 = 100 000). ALE POZOR! Na příklad 24 . 55 toto pravidlo použít nejde. Víš proč? (Správná odpověď je na konci článku)

5) Mocnina podílu

(36 : 8)2 = 362 : 82 .. analogie součinu, platí i pro podíl zapsaný zlomkem

Při umocňování součinu umocníme dělence i dělitele.
Také tady nám pravidlo ulehčí výpočty hlavně v opačném směru, tedy 406 : 206 = ?? Kolik? Vypočítej a překontroluj si svou odpověď na konci článku.

6) Mocnina mocniny

(43)2 = 43 . 43 = 46 ... Vychází opět z definice mocniny a z pravidla pro násobení mocnin.

Při umocňování mocniny se mocnitelé násobí.


Správná řešení:
1) Je třeba, aby obě mocniny měly stejné mocnitele.
2) (40 : 20)6 = 26 = 64

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