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
Autor:  Hana PilařováVydáno: 10.11.2009 14:02 Přečteno: 244090x |
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