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Réponse :

Explications étape par étape :

EXERCICE 1

A =[tex]2^{-9} *2^{5} = 2^{-4}[/tex]

C = [tex](3^{2})^{-3} *3^{4} = 3^{-2}[/tex]

B= [tex]\frac{4^{13} }{4^{14} } =4^{-1\\}[/tex]

D = [tex]3^{4} *7^{4} = 21^{4}[/tex]

EXERCICE 2

[tex]A= \frac{13^{4} *13^{5} }{13^{2} } = \frac{13^{5+4} }{13^{2} } =\frac{13^{9} }{13^{2} } = 13^{9-2} = 13^{7}[/tex]

[tex]B = \frac{6^{-5} }{6*(6^{-2})^{3} } = \frac{6^{-5} }{6*6^{(-2)*3} } = \frac{6^{-5} }{6*6^{-6} } =\frac{6^{-5} }{6^{(-6)+1} } = \frac{6^{-5} }{6^{-5} } } =6^{-5-(-5)} =6^{0}[/tex]

[tex]C = \frac{1,3*1,3^{10} }{(1,3^{2}*1.3^{3})^{2} } } = \frac{1,3^{1+10} }{(1.3^{2+3})^{2} } = \frac{1,3^{11} }{(1,3^{5})^{2} } = \frac{1,3^{11} }{1.3^{5*2} } = \frac{1,3^{11} }{1.3^{10} } = 1,3^{11-10}} = 1,3^{1}[/tex]