а) $0,25^{40} * 4^{42}$;
б) $2^{100} * (\frac{1}{2})^{103}$;
в) $(\frac{3}{4})^{50} * (\frac{4}{3})^{49}$;
г) $(-\frac{2}{3})^{24} * (\frac{3}{2})^{23}$.
$0,25^{40} * 4^{42} = 0,25^{40} * 4^{40} * 4^2 = (0,25 * 4)^{40} * 4^2 = 1^{40} * 16 = 16$
$2^{100} * (\frac{1}{2})^{103} = 2^{100} * (\frac{1}{2})^{100} * (\frac{1}{2})^{3} = (2 * \frac{1}{2})^{100} * \frac{1}{8} = 1^{100} * \frac{1}{8} = \frac{1}{8}$
$(\frac{3}{4})^{50} * (\frac{4}{3})^{49} = \frac{3}{4} * (\frac{3}{4})^{49} * (\frac{4}{3})^{49} = \frac{3}{4} * 1^{49} = \frac{3}{4}$
$(-\frac{2}{3})^{24} * (\frac{3}{2})^{23} = (\frac{2}{3})^{24} * (\frac{3}{2})^{23} = \frac{2}{3} * (\frac{2}{3})^{23} * (\frac{3}{2})^{23} = \frac{2}{3} * (\frac{2}{3} * \frac{3}{2})^{23} = \frac{2}{3} * 1 = \frac{2}{3}$
Пожауйста, оцените решение
