62 Представить в виде степени с рациональным показателем: 1 1) a. Va; 2) 62.6.3; 3) √চ:66; 4) a: Va 5) x1.7x28:√x; 6) y-3.8:y-2.3. Vy.

1. $$a^{\frac{1}{3}} \cdot \sqrt{a} = a^{\frac{1}{3}} \cdot a^{\frac{1}{2}} = a^{\frac{1}{3} + \frac{1}{2}} = a^{\frac{2+3}{6}} = a^{\frac{5}{6}}$$
2. $$b^{\frac{1}{2}} \cdot b^{\frac{1}{3}} \cdot \sqrt[6]{b} = b^{\frac{1}{2}} \cdot b^{\frac{1}{3}} \cdot b^{\frac{1}{6}} = b^{\frac{1}{2} + \frac{1}{3} + \frac{1}{6}} = b^{\frac{3+2+1}{6}} = b^{\frac{6}{6}} = b^1 = b$$
3. $$\sqrt[3]{b} : \sqrt{b^6} = b^{\frac{1}{3}} : b^{\frac{6}{2}} = b^{\frac{1}{3}} : b^3 = b^{\frac{1}{3} - 3} = b^{\frac{1-9}{3}} = b^{-\frac{8}{3}}$$
4. $$a^{\frac{4}{3}} : \sqrt{a} = a^{\frac{4}{3}} : a^{\frac{1}{2}} = a^{\frac{4}{3} - \frac{1}{2}} = a^{\frac{8-3}{6}} = a^{\frac{5}{6}}$$
5. $$x^{1.7} \cdot x^{2.8} : \sqrt{x^5} = x^{1.7+2.8} : x^{\frac{5}{2}} = x^{4.5} : x^{2.5} = x^{4.5 - 2.5} = x^2$$
6. $$y^{-3.8} : y^{-2.3} \cdot \sqrt[3]{y} = y^{-3.8 - (-2.3)} \cdot y^{\frac{1}{3}} = y^{-3.8 + 2.3} \cdot y^{\frac{1}{3}} = y^{-1.5} \cdot y^{\frac{1}{3}} = y^{-1.5 + \frac{1}{3}} = y^{-\frac{3}{2} + \frac{1}{3}} = y^{\frac{-9+2}{6}} = y^{-\frac{7}{6}}$$

Ответ:

1. $$a^{\frac{5}{6}}$$
2. $$b$$
3. $$b^{-\frac{8}{3}}$$
4. $$a^{\frac{5}{6}}$$
5. $$x^2$$
6. $$y^{-\frac{7}{6}}$$