61 Найти значение выражения: 6 1) √а. На при а =0,09; 2) √Б: Б при 6=27; 3) চি ি 6 при 6=1,3; 4) √а. Va. "Va при а =2,7.

1. $$\sqrt[3]{a} \cdot \sqrt[6]{a} = a^{\frac{1}{3}} \cdot a^{\frac{1}{6}} = a^{\frac{1}{3} + \frac{1}{6}} = a^{\frac{2}{6} + \frac{1}{6}} = a^{\frac{3}{6}} = a^{\frac{1}{2}} = \sqrt{a}$$
   При $$a = 0.09$$, $$\sqrt{0.09} = 0.3$$
2. $$\sqrt[6]{b} : \sqrt[3]{b} = b^{\frac{1}{6}} : b^{\frac{1}{3}} = b^{\frac{1}{6} - \frac{1}{3}} = b^{\frac{1}{6} - \frac{2}{6}} = b^{-\frac{1}{6}} = \frac{1}{\sqrt[6]{b}}$$
   При $$b = 27$$, $$\frac{1}{\sqrt[6]{27}} = \frac{1}{\sqrt[6]{3^3}} = \frac{1}{3^{\frac{3}{6}}} = \frac{1}{3^{\frac{1}{2}}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$$
3. $$\frac{\sqrt[3]{b} \cdot \sqrt{b^2}}{\sqrt[6]{b}} = \frac{b^{\frac{1}{3}} \cdot b^{\frac{2}{2}}}{b^{\frac{1}{6}}} = \frac{b^{\frac{1}{3}} \cdot b}{b^{\frac{1}{6}}} = b^{\frac{1}{3} + 1 - \frac{1}{6}} = b^{\frac{2+6-1}{6}} = b^{\frac{7}{6}}$$
   При $$b = 1.3$$, $$(1.3)^{\frac{7}{6}}$$
4. $$\sqrt[3]{a} \cdot \sqrt[4]{a} \cdot \sqrt[12]{a^5} = a^{\frac{1}{3}} \cdot a^{\frac{1}{4}} \cdot a^{\frac{5}{12}} = a^{\frac{1}{3} + \frac{1}{4} + \frac{5}{12}} = a^{\frac{4+3+5}{12}} = a^{\frac{12}{12}} = a^1 = a$$
   При $$a = 2.7$$, $$2.7$$

Ответ:

1. $$0.3$$
2. $$\frac{\sqrt{3}}{3}$$
3. $$(1.3)^{\frac{7}{6}}$$
4. $$2.7$$