Упр.49 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1) (3/2)^(1/3)·(2 1/4)^(1/3); 2) (3/4)^(1/4)·(6 3/4)^(1/4);
3) (15 5/8)^(1/4):(2/5)^(1/4); 4) (11 1/4)^(1/3):(3 1/3)^(1/3);
5) ((v27)^(1/3))^2; 6) (v16^(1/3))^3.

1. $$\left(\frac{3}{2}\right)^{\frac13}\cdot\left(2\frac14\right)^{\frac13} =\left(\frac{3}{2}\cdot\frac94\right)^{\frac13} =\left(\frac{27}{8}\right)^{\frac13} =\frac32.$$

2. $$\left(\frac34\right)^{\frac14}\cdot\left(6\frac34\right)^{\frac14} =\left(\frac34\cdot\frac{27}{4}\right)^{\frac14} =\left(\frac{81}{16}\right)^{\frac14} =\frac32.$$

3. $$\left(15\frac58\right)^{\frac14}:\left(\frac25\right)^{\frac14} =\left(\frac{125}{8}:\frac25\right)^{\frac14} =\left(\frac{125}{8}\cdot\frac52\right)^{\frac14} =\left(\frac{625}{16}\right)^{\frac14} =\frac52.$$

4. $$\left(11\frac14\right)^{\frac13}:\left(3\frac13\right)^{\frac13} =\left(\frac{45}{4}:\frac{10}{3}\right)^{\frac13} =\left(\frac{45}{4}\cdot\frac{3}{10}\right)^{\frac13} =\left(\frac{27}{8}\right)^{\frac13} =\frac32.$$

5. $$\left(\sqrt[3]{\sqrt{27}}\right)^2 =\sqrt[3]{\left(\sqrt{27}\right)^2} =\sqrt[3]{27} =3.$$

6. $$\left(\sqrt{\sqrt[3]{16}}\right)^3 =\sqrt{\left(\sqrt[3]{16}\right)^3} =\sqrt{16} =4.$$

Ответ

1) $$\frac32$$; 2) $$\frac32$$; 3) $$\frac52$$; 4) $$\frac32$$; 5) $$3$$; 6) $$4$$.