Задание 8. Найдите значение выражения: 1 √6⁴ 2 √5⁶ 3 √4⁵ 4 √9³ 5 √8⁴ 6 √3⁶ 7 (2√10)² / 160 8 (3√5)² / 30 9 (4√2)² / 64

Давай посчитаем каждое выражение:

1. \[ \sqrt{6^4} = 6^{4/2} = 6^2 = 36 \]

2. \[ \sqrt{5^6} = 5^{6/2} = 5^3 = 125 \]

3. \[ \sqrt{4^5} = \sqrt{(2^2)^5} = \sqrt{2^{10}} = 2^{10/2} = 2^5 = 32 \]

4. \[ \sqrt{9^3} = \sqrt{(3^2)^3} = \sqrt{3^6} = 3^{6/2} = 3^3 = 27 \]

5. \[ \sqrt{8^4} = 8^{4/2} = 8^2 = 64 \]

6. \[ \sqrt{3^6} = 3^{6/2} = 3^3 = 27 \]

7. \[ \frac{(2\sqrt{10})^2}{160} = \frac{2^2 \cdot (\sqrt{10})^2}{160} = \frac{4 \cdot 10}{160} = \frac{40}{160} = \frac{1}{4} \]

8. \[ \frac{(3\sqrt{5})^2}{30} = \frac{3^2 \cdot (\sqrt{5})^2}{30} = \frac{9 \cdot 5}{30} = \frac{45}{30} = \frac{3}{2} \]

9. \[ \frac{(4\sqrt{2})^2}{64} = \frac{4^2 \cdot (\sqrt{2})^2}{64} = \frac{16 \cdot 2}{64} = \frac{32}{64} = \frac{1}{2} \]

Ответ: 1) 36; 2) 125; 3) 32; 4) 27; 5) 64; 6) 27; 7) 1/4; 8) 3/2; 9) 1/2.