Упр.37.24 ГДЗ Мордкович 10-11 класс (Алгебра)

а) (x^-2/3 * x^5/3) / x^3/5;
б) (y^6/7 * (y^-1/2)^2) / (y^4/7)^-2;
в) (c^-2/3)^-4 / (c^1/6 * c^1/2);
г) ((a^1/2 * b^3/5) / (a^1/4 * b^2/5))^20.

1. а)

   $$\frac{x^{-\frac{2}{3}}\cdot x^{\frac{5}{3}}}{x^{\frac{3}{5}}} =x^{-\frac{2}{3}+\frac{5}{3}-\frac{3}{5}} =x^{1-\frac{3}{5}} =x^{\frac{2}{5}}$$

2. б)

   $$\frac{y^{\frac{6}{7}}\cdot \left(y^{-\frac{1}{2}}\right)^2}{\left(y^{\frac{4}{7}}\right)^{-2}} =\frac{y^{\frac{6}{7}}\cdot y^{-1}}{y^{-\frac{8}{7}}} =y^{\frac{6}{7}-1+\frac{8}{7}} =y$$

3. в)

   $$\frac{\left(c^{-\frac{2}{3}}\right)^{-4}}{c^{\frac{1}{6}}\cdot c^{\frac{1}{2}}} =\frac{c^{\frac{8}{3}}}{c^{\frac{1}{6}+\frac{1}{2}}} =\frac{c^{\frac{8}{3}}}{c^{\frac{2}{3}}} =c^2$$

4. г)

   $$\left(\frac{a^{\frac{1}{2}}\cdot b^{\frac{3}{5}}}{a^{\frac{1}{4}}\cdot b^{\frac{2}{5}}}\right)^{20} =\left(a^{\frac{1}{2}-\frac{1}{4}}\cdot b^{\frac{3}{5}-\frac{2}{5}}\right)^{20} =\left(a^{\frac{1}{4}}\cdot b^{\frac{1}{5}}\right)^{20} =a^5b^4$$

Ответ

а) $$x^{\frac{2}{5}}$$; б) $$y$$; в) $$c^2$$; г) $$a^5b^4$$.