Упр.156 ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (4-a)/8a3 * 12a5/(a2-16);
2) (4c-d)/(c2+cd) * (2c2-2d2)/(4c2-cd); Упростите выражение:
1) 3a4b3/10c5 * 4b4c2/27a7 : 5b7/9a3c3;
2) 3a2/2b2c2 : 7c8/6b3 : 9ab/14c12;
3) (5a3/b4)4 * b18/50a16;
4) (3×7/y10)4 : (3×6/y8)3.

1. $$\frac{3a^4b^3}{10c^5}\cdot\frac{4b^4c^2}{27a^7}:\frac{5b^7}{9a^3c^3}$$

   $$\frac{3a^4b^3}{10c^5}\cdot\frac{4b^4c^2}{27a^7}\cdot\frac{9a^3c^3}{5b^7}=\frac{3\cdot4\cdot9}{10\cdot27\cdot5}\cdot\frac{a^4}{a^7}\cdot\frac{a^3}{1}\cdot\frac{b^3b^4}{b^7}\cdot\frac{c^2c^3}{c^5}$$

   $$=\frac{2}{25}$$

2. $$\frac{3a^2}{2b^2c^2}:\frac{7c^8}{6b^3}:\frac{9ab}{14c^{12}}$$

   $$\frac{3a^2}{2b^2c^2}\cdot\frac{6b^3}{7c^8}\cdot\frac{14c^{12}}{9ab}$$

   $$=\frac{3\cdot6\cdot14}{2\cdot7\cdot9}\cdot\frac{a^2}{a}\cdot\frac{b^3}{b^2b}\cdot\frac{c^{12}}{c^2c^8}=2ac^2$$

3. $$\left(\frac{5a^3}{b^4}\right)^4\cdot\frac{b^{18}}{50a^{16}}$$

   $$\frac{5^4a^{12}}{b^{16}}\cdot\frac{b^{18}}{50a^{16}}=\frac{5^4}{50}\cdot\frac{b^2}{a^4}= \frac{25b^2}{2a^4}$$

4. $$\left(\frac{3x^7}{y^{10}}\right)^4:\left(\frac{3x^6}{y^8}\right)^3$$

   $$\frac{3^4x^{28}}{y^{40}}:\frac{3^3x^{18}}{y^{24}}=\frac{3^4x^{28}}{y^{40}}\cdot\frac{y^{24}}{3^3x^{18}}=3x^{10}\cdot\frac{1}{y^{16}}$$

   $$=\frac{3x^{10}}{y^{16}}$$

Ответ

1) $$\frac{2}{25}$$; 2) $$2ac^2$$; 3) $$\frac{25b^2}{2a^4}$$; 4) $$\frac{3x^{10}}{y^{16}}$$.