Вопрос:

Таблица 1. Вычислить:

Смотреть решения всех заданий с листа

Ответ:

Ответ смотри в таблице ниже!
Краткое пояснение: Для решения необходимо вспомнить свойства степеней и корней, а также уметь преобразовывать выражения с рациональными показателями.
a b c d e f g h
8 \[(\sqrt{32})^{\frac{2}{5}} = (2^{\frac{5}{2}})^{\frac{2}{5}} = 2^{\frac{5}{2} \cdot \frac{2}{5}} = 2^1 = 2\] \[4^{-\frac{3}{2}} = (2^2)^{-\frac{3}{2}} = 2^{2 \cdot (-\frac{3}{2})} = 2^{-3} = \frac{1}{2^3} = \frac{1}{8}\] \[64^{\frac{5}{6}} = (2^6)^{\frac{5}{6}} = 2^{6 \cdot \frac{5}{6}} = 2^5 = 32\] \[32^{-\frac{3}{5}} = (2^5)^{-\frac{3}{5}} = 2^{5 \cdot (-\frac{3}{5})} = 2^{-3} = \frac{1}{2^3} = \frac{1}{8}\] \[(\sqrt{27})^{\frac{2}{3}} = (3^{\frac{3}{2}})^{\frac{2}{3}} = 3^{\frac{3}{2} \cdot \frac{2}{3}} = 3^1 = 3\] \[32^{\frac{4}{5}} = (2^5)^{\frac{4}{5}} = 2^{5 \cdot \frac{4}{5}} = 2^4 = 16\] \[(\sqrt{8})^{\frac{2}{3}} = (2^{\frac{3}{2}})^{\frac{2}{3}} = 2^{\frac{3}{2} \cdot \frac{2}{3}} = 2^1 = 2\] \[16^{-\frac{3}{4}} = (2^4)^{-\frac{3}{4}} = 2^{4 \cdot (-\frac{3}{4})} = 2^{-3} = \frac{1}{2^3} = \frac{1}{8}\]
7 \[4^{-\frac{1}{2}} = (2^2)^{-\frac{1}{2}} = 2^{2 \cdot (-\frac{1}{2})} = 2^{-1} = \frac{1}{2}\] \[(\frac{1}{9})^{-\frac{1}{2}} = (\frac{1}{3^2})^{-\frac{1}{2}} = (3^{-2})^{-\frac{1}{2}} = 3^{-2 \cdot (-\frac{1}{2})} = 3^1 = 3\] \[125^{-\frac{1}{3}} = (5^3)^{-\frac{1}{3}} = 5^{3 \cdot (-\frac{1}{3})} = 5^{-1} = \frac{1}{5}\] \[(\frac{1}{8})^{\frac{1}{3}} = (\frac{1}{2^3})^{\frac{1}{3}} = (2^{-3})^{\frac{1}{3}} = 2^{-3 \cdot \frac{1}{3}} = 2^{-1} = \frac{1}{2}\] \[16^{-\frac{1}{4}} = (2^4)^{-\frac{1}{4}} = 2^{4 \cdot (-\frac{1}{4})} = 2^{-1} = \frac{1}{2}\] \[(\frac{1}{16})^{-\frac{1}{2}} = (\frac{1}{4^2})^{-\frac{1}{2}} = (4^{-2})^{-\frac{1}{2}} = 4^{-2 \cdot (-\frac{1}{2})} = 4^1 = 4\] \[81^{-\frac{1}{4}} = (3^4)^{-\frac{1}{4}} = 3^{4 \cdot (-\frac{1}{4})} = 3^{-1} = \frac{1}{3}\] \[(\frac{1}{27})^{-\frac{1}{3}} = (\frac{1}{3^3})^{-\frac{1}{3}} = (3^{-3})^{-\frac{1}{3}} = 3^{-3 \cdot (-\frac{1}{3})} = 3^1 = 3\]
6 \[16^{\frac{1}{4}} = (2^4)^{\frac{1}{4}} = 2^{4 \cdot \frac{1}{4}} = 2^1 = 2\] \[64^{\frac{1}{2}} = (8^2)^{\frac{1}{2}} = 8^{2 \cdot \frac{1}{2}} = 8^1 = 8\] \[8^{\frac{1}{3}} = (2^3)^{\frac{1}{3}} = 2^{3 \cdot \frac{1}{3}} = 2^1 = 2\] \[32^{\frac{1}{5}} = (2^5)^{\frac{1}{5}} = 2^{5 \cdot \frac{1}{5}} = 2^1 = 2\] \[27^{\frac{1}{3}} = (3^3)^{\frac{1}{3}} = 3^{3 \cdot \frac{1}{3}} = 3^1 = 3\] \[81^{\frac{1}{4}} = (3^4)^{\frac{1}{4}} = 3^{4 \cdot \frac{1}{4}} = 3^1 = 3\] \[64^{\frac{1}{3}} = (4^3)^{\frac{1}{3}} = 4^{3 \cdot \frac{1}{3}} = 4^1 = 4\] \[25^{\frac{1}{2}} = (5^2)^{\frac{1}{2}} = 5^{2 \cdot \frac{1}{2}} = 5^1 = 5\]
5 \[(\sqrt{7})^2 = 7^{\frac{1}{2} \cdot 2} = 7^1 = 7\] \[(\sqrt{2})^8 = 2^{\frac{1}{2} \cdot 8} = 2^4 = 16\] \[(\sqrt{5})^4 = 5^{\frac{1}{2} \cdot 4} = 5^2 = 25\] \[(\sqrt{2})^{10} = 2^{\frac{1}{2} \cdot 10} = 2^5 = 32\] \[(\sqrt{6})^4 = 6^{\frac{1}{2} \cdot 4} = 6^2 = 36\] \[(\sqrt{2})^6 = 2^{\frac{1}{2} \cdot 6} = 2^3 = 8\] \[(\sqrt{3})^6 = 3^{\frac{1}{2} \cdot 6} = 3^3 = 27\] \[(\sqrt{5})^0 = 1\]
4 \[(\frac{3}{2})^{-3} = (\frac{2}{3})^3 = \frac{2^3}{3^3} = \frac{8}{27}\] \[(\frac{2}{5})^{-2} = (\frac{5}{2})^2 = \frac{5^2}{2^2} = \frac{25}{4}\] \[(\frac{3}{4})^{-3} = (\frac{4}{3})^3 = \frac{4^3}{3^3} = \frac{64}{27}\] \[(\frac{1}{2})^{-5} = 2^5 = 32\] \[(\frac{1}{3})^{-1} = 3^1 = 3\] \[(\frac{2}{3})^{-4} = (\frac{3}{2})^4 = \frac{3^4}{2^4} = \frac{81}{16}\] \[(\frac{3}{4})^{-1} = \frac{4}{3}\] \[(\frac{1}{2})^{-4} = 2^4 = 16\]
3 \[6^{-2} = \frac{1}{6^2} = \frac{1}{36}\] \[2^{-4} = \frac{1}{2^4} = \frac{1}{16}\] \[3^{-3} = \frac{1}{3^3} = \frac{1}{27}\] \[5^{-1} = \frac{1}{5}\] \[3^{-4} = \frac{1}{3^4} = \frac{1}{81}\] \[2^{-3} = \frac{1}{2^3} = \frac{1}{8}\] \[7^{-2} = \frac{1}{7^2} = \frac{1}{49}\] \[4^{-1} = \frac{1}{4}\]
2 \[(\frac{1}{2})^5 = \frac{1^5}{2^5} = \frac{1}{32}\] \[(\frac{2}{3})^3 = \frac{2^3}{3^3} = \frac{8}{27}\] \[(\frac{3}{5})^2 = \frac{3^2}{5^2} = \frac{9}{25}\] \[(\frac{3}{2})^1 = \frac{3}{2}\] \[(\frac{4}{3})^3 = \frac{4^3}{3^3} = \frac{64}{27}\] \[(\frac{1}{3})^4 = \frac{1^4}{3^4} = \frac{1}{81}\] \[(\frac{2}{5})^3 = \frac{2^3}{5^3} = \frac{8}{125}\] \[(\frac{3}{4})^2 = \frac{3^2}{4^2} = \frac{9}{16}\]
1 \[3^4 = 81\] \[4^3 = 64\] \[2^4 = 16\] \[5^3 = 125\] \[2^5 = 32\] \[3^3 = 27\] \[5^0 = 1\] \[2^3 = 8\]
Ответ смотри в таблице выше!

Результат: Ты – Цифровой атлет! Уровень интеллекта: +50. Минус 15 минут нудной домашки. Потрать их на катку или новый рилс. Стань легендой класса: поделись решением с теми, кто в танке.

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