Question

Найдите значение выражения:а)5^-7*2^-8/10^-5 б)3^-20*9^-33/27^-33*81 в)7^-25*49^-52/49-^35*7^-60 г)3^-14*5^-14/225^-6*45^-2

Answer 1

$frac{5^{-7}*2^{-8}}{10^{-5}}= frac{5^{5}*2^{5}}{5^{7}*2^{8}}= frac{1}{5^{2}*2^{3}} = frac{1}{200} =0.005$

$frac{3^{-20}*9^{-33}}{27^{-33}}= frac{3^{33}*9^{33}}{3^{20}*9^{33}} = 3^{13}$

$frac{7^{-25}*49^{-52}}{49^{-35}*7^{-60}} = frac{49^{35}*7^{60}}{49^{52}*7^{25}} = frac{7^{35}}{49^{17}} = frac{7^{35}}{(7^{2})^{17}} = frac{7^{35}}{7^{34}} =7$

$frac{3 ^{-14}*5^{-14} }{225^{-6}*45^{-2}} = frac{225^{6}*45^{2}}{5^{14} *3 ^{14}} = frac{(15^{2})^{6}*15^{2}*3^{2} }{15^{14}}= frac{15^{14}*3^{2} }{15^{14}} =3^{2}=9$