[tex]a)\\4^{8} = (2^{2})^{8} = 2^{16}\\\\2^{16} > 2^{12}\\\\\boxed{4^{8} > 2^{12}}[/tex]
[tex]b)\\9^{3} = (3^{2})^{3} = 3^{6}\\\\27^{2} = (3^{3})^{2} = 3^{6}\\\\\boxed{9^{3} = 27^{2}}[/tex]
[tex]c)\\25^{3} = (5^{2})^{3} = 5^{6}\\\\125^{2} = (5^{3})^{2} = 5^{6}\\\\\boxed{25^{3} = 125^{2}}[/tex]
[tex]d)\\8^{5} = (2^{3})^{5} = 2^{15}\\\\4^{7} = (2^{2})^{7} = 2^{14}\\\\2^{15} > 2^{14}\\\\\boxed{8^{5} > 4^{7}}[/tex]
[tex]e)\\100^{5} = (10^{2})^{5} = 10^{10}\\\\1000^{2} = (10^{3})^{2} = 10^{6}\\\\10^{10} > 10^{6}\\\\\boxed{100^{5} > 1000^{2}}[/tex]
[tex]f)\\36^{3} = (6^{2})^{3} = 6^{6}\\\\6^{6} > 6^{5}\\\\\boxed{36^{3} > 6^{5}}[/tex]
Wyjaśnienie:
Potęga potęgi jest równa potędze o tej samej podstawie a i wykładniku równym iloczynowi danych wykładników n i m.
[tex](a^{n})^{m} = a^{n\cdot m} \ \ \ \ \ \ \ \ \ a \in R, n,m \in N[/tex]
