Страница 46 номер 124, ГДЗ по алгебре за 10-11 класс Алимов - ответы и решение
Сравнить значения выражений: 1) \(3{,}1^7\) и \(4{,}3^7\); 2) \(\left(\frac{10}{11}\right)^3\) и \(\left(\frac{12}{11}\right)^3\); 3) \(0{,}3^8\) и \(0{,}2^8\); 4) \(2{,}5^2\) и \(2{,}6^2\); 5) \(\left(\frac{7}{9}\right)^{-2}\) и \(\left(\frac{8}{10}\right)^{-2}\); 6) \(\left(\frac{14}{15}\right)^{-6}\) и \(\left(\frac{15}{16}\right)^{-6}\); 7) \((4\sqrt{3})^{-3}\) и \((3\sqrt{4})^{-3}\); 8) \((2\sqrt[3]{6})^{-5}\) и \((6\sqrt[3]{2})^{-5}\).
1) \(3{,}1^{7} < 4{,}3^{7}\), т.к. \(3{,}1 < 4{,}3\);
2) \(\left(\frac{10}{11}\right)^{3} < \left(\frac{12}{11}\right)^{3}\), т.к. \(\frac{10}{11} < \frac{12}{11}\);
3) \(0{,}3^{8} > 0{,}2^{8}\), т.к. \(0{,}3 > 0{,}2\);
4) \(2{,}5^{2} < 2{,}6^{2}\), т.к. \(2{,}5 < 2{,}6\);
5) \(\left(\frac{7}{9}\right)^{-2} > \left(\frac{8}{10}\right)^{-2}\), т.к. \(\frac{7}{9} = \frac{70}{90} < \frac{72}{90} = \frac{8}{10}\) и \(-2 < 0\);
6) \(\left(\frac{14}{15}\right)^{-6} > \left(\frac{15}{16}\right)^{-6}\), т.к. \(\frac{14}{15} = \frac{224}{240} < \frac{225}{240} = \frac{15}{16}\) и \(-6 < 0\);
7) \(\left(4\sqrt{3}\right)^{-3} < \left(3\sqrt{4}\right)^{-3}\), т.к. \(4\sqrt{3} = \sqrt{48} > \sqrt{36} = 3\sqrt{4}\) и \(-3 < 0\);
8) \(\left(2\sqrt[3]{6}\right)^{-5} > \left(6\sqrt[3]{2}\right)^{-5}\), т.к. \(2\sqrt[3]{6} = \frac{12\sqrt[3]{6}}{6} = \frac{12}{\sqrt[3]{6^{2}}} < 6\sqrt[3]{2} = \frac{12}{\sqrt[3]{2^{2}}}\) и \(-5 < 0\).
