Упр.52 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1) (2ab)^(1/3)·(4a^2 b)^(1/3)·(27b)^(1/3);
2) (abc)^(1/4)·(a^3 b^2 c)^(1/4)·(b^5 c^2)^(1/4);
3) ((a^3 b^2)^(1/5)·(3a^2 b^3)^(1/5))/3^(1/5);
4) ((8x^2 y^5)·(4x^3 y))/(2xy^2)^(1/4).

1. $$\sqrt[3]{2ab}\cdot \sqrt[3]{4a^2b}\cdot \sqrt[3]{27b} = \sqrt[3]{2ab\cdot 4a^2b\cdot 27b} = \sqrt[3]{216a^3b^3}$$

   $$\sqrt[3]{216a^3b^3}=6ab$$

2. $$\sqrt[4]{abc}\cdot \sqrt[4]{a^3b^2c}\cdot \sqrt[4]{b^5c^2} = \sqrt[4]{a^4b^8c^4}$$

   $$\sqrt[4]{a^4b^8c^4}=ab^2c$$

3. $$\frac{\sqrt[5]{a^3b^2}\cdot \sqrt[5]{3a^2b^3}}{\sqrt[5]{3}} = \sqrt[5]{\frac{a^3b^2\cdot 3a^2b^3}{3}} = \sqrt[5]{a^5b^5}$$

   $$\sqrt[5]{a^5b^5}=ab$$

4. $$\frac{\sqrt[4]{8x^2y^5}\cdot \sqrt[4]{4x^3y}}{\sqrt[4]{2xy^2}} = \sqrt[4]{\frac{8x^2y^5\cdot 4x^3y}{2xy^2}} = \sqrt[4]{16x^4y^4}$$

   $$\sqrt[4]{16x^4y^4}=2xy$$

Ответ

1) $$6ab$$; 2) $$ab^2c$$; 3) $$ab$$; 4) $$2xy$$.