Szczegółowe wyjaśnienie:
Korzystamy z własności potęgowania:
[tex]a^{n}\cdot b^{n} = (a\cdot b)^{n}[/tex]
[tex]2^{4}\cdot3^{2} = (2^{2})^{2}\cdot3^{2} = 4^{2}\cdot3^{2} = (4\cdot3)^{2} = 12^{2} \ \ \ \ \ \ \boxed{P}\\\\2^{4}\cdot3^{4} = (2\cdot3)^{4} = 6^{4} \neq 5^{4} \ \ \ \ \ \ \ \boxed{ F}\\\\2^{4}\cdot3^{4} = (2\cdot3)^{4} = 6^{4} \ \ \ \ \ \ \boxed{P}\\\\2^{4}\cdot3^{2} = (2^{2})^{2}\cdot3^{2} = 4^{2}\cdot3^{2} = (4\cdot3)^{2} = 12^{2} \neq 5^{6} \ \ \ \ \ \ \boxed{F}[/tex]
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Szczegółowe wyjaśnienie:
Korzystamy z własności potęgowania:
[tex]a^{n}\cdot b^{n} = (a\cdot b)^{n}[/tex]
[tex]2^{4}\cdot3^{2} = (2^{2})^{2}\cdot3^{2} = 4^{2}\cdot3^{2} = (4\cdot3)^{2} = 12^{2} \ \ \ \ \ \ \boxed{P}\\\\2^{4}\cdot3^{4} = (2\cdot3)^{4} = 6^{4} \neq 5^{4} \ \ \ \ \ \ \ \boxed{ F}\\\\2^{4}\cdot3^{4} = (2\cdot3)^{4} = 6^{4} \ \ \ \ \ \ \boxed{P}\\\\2^{4}\cdot3^{2} = (2^{2})^{2}\cdot3^{2} = 4^{2}\cdot3^{2} = (4\cdot3)^{2} = 12^{2} \neq 5^{6} \ \ \ \ \ \ \boxed{F}[/tex]