Question

Vă rog ajutați-mă dau coroană 20 de puncte și mă abonez!

Answer 1

$a)3^{17}\cdot5^{23}:3^{7}=3^{17}\cdot5^{23}\cdot3^{-7}=3^{17-7}\cdot5^{23}=3^{10}\cdot5^{23}\\ \\b)2^{41}\cdot3^{17}:2^{15}\cdot3^{7}=2^{41-15}\cdot3^{17-7}=2^{26}\cdot3^{10}\\ \\c)(2^{49}\cdot3^{21}\cdot5^{17}):(2^{7}\cdot3^{4})\cdot5^{16}=2^{49-7}\cdot3^{21-4}\cdot5^{17-16})=2^{42}\cdot3^{17}\cdot5$

$d)(3^{17}\cdot5^{23}\cdot7^{5}):(3^{17}\cdot5^{23})=7^{5}$

$e)(2^{31}\cdot3^{29}\cdot5^{11}):(2^{11}\cdot3^{10})\cdot5^{11}=2^{31-11}\cdot3^{29-10}\cdot5^{11-11})=2^{20}\cdot3^{19}\cdot1$

$f)(3^{7}\cdot5^{9})^{2}:3^{12}\cdot5^{17}=(3^{7\cdot2}\cdot5^{9\cdot2}):(3^{12}\cdot5^{17}=3^{14-12}\cdot5^{18-17}=3^{2}\cdot5^{1}=9\cdot5=45$

$g)(5^{7}\cdot7^{3}\cdot2)^{10}:(5^{4}\cdot2)^{8}=(5^{7\cdot10}\cdot7^{3\cdot10}\cdot2^{10}):(5^{4\cdot8}\cdot2^{8})=5^{70-32}\cdot7^{40}\cdot2^{10-8}=5^{38}\cdot7^{40}\cdot2^{2}$

$h)(2^{5}\cdot3^{7}\cdot5^{4})^{10}:(4^{25}\cdot3^{68}\cdot25^{2})=(2^{5\cdot10}\cdot3^{7\cdot10}\cdot5^{4\cdot10}):(2^{2\cdot25}\cdot3^{68}\cdot5^{2\cdot2})=2^{50}\cdot3^{70}\cdot5^{40}:2^{50}\cdot3^{68}\cdot5^{4}=2^{50-50}\cdot3^{70-68}\cdot5^{40-4}=2^{0}\cdot3^{2}\cdot5^{36}=3^{2}\cdot5^{36}$