Question

Comparați următoarele puteri : 2^41 ,4^21 , 16^11 , 25^17 , 5^33 , 125^12

Answer 1

$2^{41};(2^{2})^{21}=2^{2\cdot21}=2^{42};(2^{4})^{11}=2^{4\cdot11}=2^{44}\\ \\2^{41}<2^{42}<2^{44}\\ \\2^{41}<4^{21}<16^{11}$

$25^{17}=(5^{2})^{17}=5^{2\cdot17)}=5^{34} \\ \\5^{33}=\\ \\ 125^{12}=(5^{3})^{12}=5^({3\cdot12)}=5^{36} \\ \\5^{33}<5^{34}<5^{36} \\ \\5^{33}<25^{17}<125^{12}$