Сравните значения выражений:
а) $(\frac{2}{3})^5 * (\frac{3}{2})^5$ и $(1,5 + \frac{2}{3})^0$;
б) $(\frac{2}{3})^7 * (\frac{3}{2})^6$ и $(1,5 + \frac{2}{3})^0$;
в) $(-\frac{2}{3})^9 * 1,5^{10}$ и $(-\frac{3}{2} - \frac{2}{3})^0$;
г) $(\frac{2}{3})^3 * (-1,5)^4$ и $(\frac{3}{2} - \frac{2}{3})^0$.
$(\frac{2}{3})^5 * (\frac{3}{2})^5 = (\frac{2}{3} * \frac{3}{2})^5 = 1^5 = 1$;
$(1,5 + \frac{2}{3})^0 = 1$;
1 = 1;
$(\frac{2}{3})^5 * (\frac{3}{2})^5 = (1,5 + \frac{2}{3})^0$.
$(\frac{2}{3})^7 * (\frac{3}{2})^6 = \frac{2}{3} * (\frac{2}{3})^6 * (\frac{3}{2})^6 = \frac{2}{3} * (\frac{2}{3} * \frac{3}{2})^6 = \frac{2}{3} * 1^6 = \frac{2}{3}$;
$(1,5 + \frac{2}{3})^0 = 1$;
$\frac{2}{3} < 1$;
$(\frac{2}{3})^7 * (\frac{3}{2})^6 < (1,5 + \frac{2}{3})^0$.
$(-\frac{2}{3})^9 * 1,5^{10} = (-\frac{2}{3})^9 * (\frac{3}{2})^{10} = (-\frac{2}{3})^9 * (\frac{3}{2})^{9} * \frac{3}{2} = (-\frac{2}{3} * \frac{3}{2})^9 * \frac{3}{2} = (-1)^9 * 1,5 = -1,5$;
$(-\frac{3}{2} - \frac{2}{3})^0 = 1$;
−1,5 < 1;
$(-\frac{2}{3})^9 * 1,5^{10} < (-\frac{3}{2} - \frac{2}{3})^0$.
$(\frac{2}{3})^3 * (-1,5)^4 = (\frac{2}{3})^3 * (-\frac{3}{2})^4 = (\frac{2}{3})^3 * (-\frac{3}{2})^3 * (-\frac{3}{2}) = (\frac{2}{3} * (-\frac{3}{2}))^3 * (-1,5) = (-1)^3 * (-1,5) = 1,5$;
$(\frac{3}{2} - \frac{2}{3})^0 = 1$;
1,5 > 0;
$(\frac{2}{3})^3 * (-1,5)^4 > (\frac{3}{2} - \frac{2}{3})^0$.
Пожауйста, оцените решение