Упр.1.2 ГДЗ Мерзляк 11 класс Базовый уровень (Алгебра)

1) 5^(v3-1)^2 : (1/5)^(2v3);
2) ((v2)^(v6))^(v6);
3) ((10^(1/5))^(v5))^(-2v5).

1. $$5^{(\sqrt{3}-1)^2} : \left(\frac{1}{5}\right)^{2\sqrt{3}} = 5^{(\sqrt{3}-1)^2} \cdot 5^{2\sqrt{3}}$$

   $$ (\sqrt{3}-1)^2 = 3 — 2\sqrt{3} + 1 = 4 — 2\sqrt{3} $$

   $$5^{4-2\sqrt{3}} \cdot 5^{2\sqrt{3}} = 5^4 = 625$$

2. $$\left(\left(\sqrt{2}\right)^{\sqrt{6}}\right)^{\sqrt{6}} = \left(\sqrt{2}\right)^{\sqrt{6}\cdot\sqrt{6}} = \left(\sqrt{2}\right)^6$$

   $$\left(\sqrt{2}\right)^6 = \left(2^{1/2}\right)^6 = 2^3 = 8$$

3. $$\left(\left(\sqrt[5]{10}\right)^{\sqrt{5}}\right)^{-2\sqrt{5}} = \left(\sqrt[5]{10}\right)^{-2\sqrt{5}\cdot\sqrt{5}} = \left(\sqrt[5]{10}\right)^{-10}$$

   $$\left(\sqrt[5]{10}\right)^{-10} = \left(10^{1/5}\right)^{-10} = 10^{-2} = \frac{1}{100} = 0{,}01$$

Ответ

1) $$625$$; 2) $$8$$; 3) $$0{,}01$$.