Упр.29 ГДЗ Алимов 10-11 класс (Алгебра)

1. $$\sqrt[3]{10^6}$$
2. $$\sqrt[3]{3^{12}}$$
3. $$\sqrt[4]{\left(\frac{1}{2}\right)^{12}}$$
4. $$\sqrt[4]{\left(\frac{1}{3}\right)^{16}}$$

1. $$\sqrt[3]{10^6}=\sqrt[3]{(10^2)^3}=10^2=100.$$

2. $$\sqrt[3]{3^{12}}=\sqrt[3]{(3^4)^3}=3^4=81.$$

3. $$\sqrt[4]{\left(\frac12\right)^{12}}=\sqrt[4]{\left(\left(\frac12\right)^3\right)^4}=\left(\frac12\right)^3=\frac18.$$

4. $$\sqrt[4]{\left(\frac13\right)^{16}}=\sqrt[4]{\left(\left(\frac13\right)^4\right)^4}=\left(\frac13\right)^4=\frac1{81}.$$

Ответ: $$100;\ 81;\ \frac18;\ \frac1{81}.$$