Упр.49 ГДЗ Колягин Ткачёва 9 класс (Алгебра)
- Вычислить:
1) $$\left(\frac{3}{2}\right)^{\frac{1}{3}}\cdot\left(2\frac{1}{4}\right)^{\frac{1}{3}}$$;
2) $$\left(\frac{3}{4}\right)^{\frac{1}{4}}\cdot\left(6\frac{3}{4}\right)^{\frac{1}{4}}$$;
3) $$\left(15\frac{5}{8}\right)^{\frac{1}{4}}:\left(\frac{2}{5}\right)^{\frac{1}{4}}$$;
4) $$\left(11\frac{1}{4}\right)^{\frac{1}{3}}:\left(3\frac{1}{3}\right)^{\frac{1}{3}}$$;
5) $$\left(\left(\sqrt{27}\right)^{\frac{1}{3}}\right)^2$$;
6) $$\left(\left(\sqrt{16}\right)^{\frac{1}{3}}\right)^3$$.
$$\left(\frac{3}{2}\right)^{\frac13}\cdot\left(2\frac14\right)^{\frac13} =\left(\frac{3}{2}\cdot\frac94\right)^{\frac13} =\left(\frac{27}{8}\right)^{\frac13} =\frac32.$$
$$\left(\frac34\right)^{\frac14}\cdot\left(6\frac34\right)^{\frac14} =\left(\frac34\cdot\frac{27}{4}\right)^{\frac14} =\left(\frac{81}{16}\right)^{\frac14} =\frac32.$$
$$\left(15\frac58\right)^{\frac14}:\left(\frac25\right)^{\frac14} =\left(\frac{125}{8}:\frac25\right)^{\frac14} =\left(\frac{125}{8}\cdot\frac52\right)^{\frac14} =\left(\frac{625}{16}\right)^{\frac14} =\frac52.$$
$$\left(11\frac14\right)^{\frac13}:\left(3\frac13\right)^{\frac13} =\left(\frac{45}{4}:\frac{10}{3}\right)^{\frac13} =\left(\frac{45}{4}\cdot\frac{3}{10}\right)^{\frac13} =\left(\frac{27}{8}\right)^{\frac13} =\frac32.$$
$$\left(\sqrt[3]{\sqrt{27}}\right)^2 =\sqrt[3]{\left(\sqrt{27}\right)^2} =\sqrt[3]{27} =3.$$
$$\left(\sqrt{\sqrt[3]{16}}\right)^3 =\sqrt{\left(\sqrt[3]{16}\right)^3} =\sqrt{16} =4.$$
Ответ
1) $$\frac32$$; 2) $$\frac32$$; 3) $$\frac52$$; 4) $$\frac32$$; 5) $$3$$; 6) $$4$$.
