Пожалуйста решите номер 594

а) 0,25 = [latex] \frac{25}{100} = \frac{1}{4} [/latex] [latex] \frac{1}{4} = 4^{-1} [/latex] [latex] 4^{-40} * 4^{42} = 4^{-40+42} = 4^{2} = 16 [/latex] б) [latex] \frac{1}{2} = 2^{-1} [/latex] [latex] 2^{100} * 2^{-103} = 2^{100+(-103)} = 2^{-3} = (\frac{1}{2}) ^{3} = \frac{1}{8} [/latex] в) [latex] (\frac{4}{3}) ^{49} = (\frac{3}{4}) ^{-49} [/latex] [latex] ( \frac{3}{4}) ^{50} * ( \frac{3}{4}) ^{-49} = ( \frac{3}{4}) ^{50+(-49)} = \frac{3}{4} [/latex] г) [latex] ( \frac{3}{2}) ^{23} = ( \frac{2}{3}) ^{-23} [/latex] [latex]- (\frac{2}{3}) ^{24} * (\frac{2}{3}) ^{-23} = - (\frac{2}{3}) ^{24+ (-23)} = -\frac{2}{3}[/latex]