Question

Вычислить: б) 25^4*5/125^3 в) 128^5/32^4*64^2 г) 6^12/(2^5*3^7)^2 д) 21^8/9^7*7^9 е) 125^3*81^2/15^10 ж) 0,125^12*2^37 з) (1/3) ^17*81^4 и) (3/5)^27*(125/27)^8

Answer 1

$\frac{25 ^{4} *5}{125 ^{3} }= \frac{(5 ^{2}) ^{4} *5 }{(5 ^{3}) ^{3}} = \frac{ 5^{8} *5}{5 ^{9} }= \frac{5 ^{9} }{5 ^{9} } =1\\\\ \frac{ 128^{5} }{ 32^{4} *64 ^{2} } = \frac{(2 ^{7}) ^{5}}{(2 ^{5}) ^{4} *(2 ^{6}) ^{2}}= \frac{2 ^{35} }{2 ^{20}*2 ^{12}} =2 ^{35-20-12}=2 ^{3} =8\\\\ \frac{6 ^{12} }{( 2^{5}* 3^{7} ) ^{2}} = \frac{2 ^{12}*3 ^{12}}{2 ^{10}*3 ^{14}}=2 ^{12-10} *3 ^{12-14} =2 ^{2}*3 ^{-2}=4* \frac{1}{9}= \frac{4}{9}\\\\ \frac{21 ^{8} }{9 ^{7}*7 ^{9}}= \frac{ 3^{8}* 7^{8} }{3 ^{14}* 7^{9}}= \frac{1}{3 ^{6} *7}= \frac{1}{729*7}= \frac{1}{5103}\\\\ \frac{ 125^{3}* 81^{2}}{ 15^{10} }= \frac{( 5^{3} ) ^{3}*(3 ^{4}) ^{2} }{3 ^{10}*5 ^{10} }= \frac{ 5^{9}* 3^{8} }{3 ^{10}* 5^{10}} = \frac{1}{3 ^{2}*5 } = \frac{1}{45}\\\\0,125 ^{12} *2 ^{37}= \frac{( 5^{3}) ^{12}*2 ^{37}}{(2 ^{3}) ^{12} *( 5^{3}) ^{12}} = \frac{ 5^{36}* 2^{37}}{ 2^{36}* 5^{36}}=2\\\\( \frac{1}{3} ) ^{17}* 81^{4}= \frac{(3 ^{4}) ^{4}}{ 3^{17} }= \frac{3 ^{16} }{ 3^{17} }= \frac{1}{3}\\\\( \frac{3}{5}) ^{27} *( \frac{125}{27}) ^{8} = \frac{3 ^{27}*(5 ^{3}) ^{8} }{5 ^{27}*( 3^{3}) ^{8}} = \frac{3 ^{27} *5 ^{24} }{5 ^{27}* 3 ^{24} }= \frac{ 3^{3} }{5 ^{3} }= \frac{27}{125}$