Răspuns:
Explicație pas cu pas:
[tex]5^{14} = 5^{2\cdot 7} = (5^2)^7 = 25^7 < 32^7 = (2^5)^7 = 2^{5\cdot 7} = 2^{35}[/tex]
[tex]10^{40} > 9^{40} = (3^2)^{40} = 3^{2\cdot 40} = 3^{80}[/tex]
[tex]3^{15} = 3^{3\cdot 5} = (3^3)^5 = 27^5 > 16^5 = (2^4)^5 = 2^{4\cdot 5} = 2^{20}[/tex]
[tex]3^{39} = 3^{3\cdot 13} = (3^3)^{13} = 27^{13} > 16^{13} = (4^2)^{13} = 4^{2\cdot 13} = 4^{26}[/tex]
[tex]7^{10} = 7^{2\cdot 5} = (7^2)^{5} = 49^{5} < 64^{5} = (4^3)^{5} = 4^{3\cdot 5} = 4^{15}[/tex]
[tex]26^{4} = 26^{2\cdot 2} = (26^2)^{2} = 676^{2} < 729^{2} = (9^3)^{2} = 9^{3\cdot 2} = 9^{6}[/tex]
[tex]30^{20} = 30^{2\cdot 10} = (30^2)^{10} = 900^{10} < 8000^{10} = (20^3)^{10} = 20^{3\cdot 10} = 20^{30}[/tex]
[tex]6^{22} = 6^{2\cdot 11} = (6^2)^{11} = 36^{11} > 27^{11} = (3^3)^{11} = 3^{3\cdot 11} = 3^{33}[/tex]
[tex]2^{111} = 2^{3\cdot 37} = (2^3)^{37} = 8^{37} < 81^{37} = (9^2)^{37} = 9^{2\cdot 37} = 9^{74}[/tex]
[tex]13^{46} = 13^{2\cdot 23} = (13^2)^{23} = 169^{23} > 125^{23} = (5^3)^{23} = 5^{3\cdot 23} = 5^{69}[/tex]
[tex]10^{41} < 512^{41} = (8^3)^{41} = 8^{3\cdot 41} = 8^{123}[/tex]
[tex]3^{4}=3^{2\cdot 2} = (3^2)^{2} = 9^2 > 8^{2} = (2^3)^{2}= 2^{3\cdot 2} = 2^{2\cdot 3} =(2^2)^{3} = 4^{3}[/tex]
[tex]25^{18} = 25^{2\cdot 9} = (25^2)^{9} = 625^{9} > 512^{9} = (8^3)^{9} = 8^{3\cdot 9} = 8^{27}[/tex]
[tex]4^{48} = 4^{4\cdot 12} = (4^4)^{12} = 256^{12} > 216^{12} = (6^3)^{12} = 6^{3\cdot 12} = 6^{36}[/tex]
[tex]5^{51} = 5^{3\cdot 17} = (5^3)^{17} = 125^{17} < 128^{17} = (2^7)^{17} = 2^{7\cdot 17} = 2^{119}[/tex]
