Question

Salut. Exercițiul 1 de la probleme propuse vă rog. E ok dacă crezi că este prea lung. :)

Answer 1

$a)7^{10}\cdot8^{10} =(7\cdot8)^{10}=56^{10}\\ \\b)11^{8}\cdot5^{8} =(5\cdot11)^{8} =55^{8}\\ \\c)3^{10}\cdot 5^{10}\cdot 7^{10} =(3\cdot5\cdot7)^{10} =105^{10}\\ \\d)15^{25}\cdot4^{25}\cdot7^{25}=(15\cdot4\cdot7)^{25} =420^{25}\\ \\e) 32^{78}\cdot25^{78} =(32\cdot25)^{78} =800^{78}$

$f)6^{35}\cdot5^{35}\cdot30^{35} =(6\cdot5\cdot30)^{35} =900^{35}$

$g)2^{18}\cdot4^{18}\cdot3^{18}\cdot5^{18} =(2\cdot3\cdot4\cdot5})^{18}=120^{18}$

$h)425^{62}:25^{62}=(17\cdot25)^{62}:25^{62} =17^{62}$

$i)64^{125}:16^{125}\\ \\(4\cdot16)^{125}:16^{125}=(16^{125}\cdot4^{125}): 16^{125}=4^{125}$

$j) 225^{45}:15^{45}:5^{45}=\\ \\(15^{45}\cdot15^{45}):15^{45}:5^{45}=15^{45}:5^{45}=\\ \\=(3\cdot4)^{45}:5^{45} =3^{45}$

$k)130^{81}:26^{81}=(\frac{130}{26})^{81} =\frac{65}{13}^{81}$