Упр.154 ГДЗ Мерзляк Полонский 8 класс (Алгебра)

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. Представьте в виде дроби выражение:
1) (a6/b3)10;
2) (-4m/9n3)2;
3) (-10c7/3d5)3;
4) (2m3n2/kp8)6.

1. $$\frac{3a^4b^3}{10c^5}\cdot\frac{4b^4c^2}{27a^7}:\frac{5b^7}{9a^3c^3}$$
   $$=\frac{3a^4b^3}{10c^5}\cdot\frac{4b^4c^2}{27a^7}\cdot\frac{9a^3c^3}{5b^7}$$
   $$=\frac{3\cdot4\cdot9}{10\cdot27\cdot5}\cdot a^{4-7+3}\cdot b^{3+4-7}\cdot c^{2-5+3}$$
   $$=\frac{2}{25}.$$
2. $$\frac{3a^2}{2b^2c^2}:\frac{7c^8}{6b^3}:\frac{9ab}{14c^{12}}$$
   $$=\frac{3a^2}{2b^2c^2}\cdot\frac{6b^3}{7c^8}\cdot\frac{14c^{12}}{9ab}$$
   $$=\frac{3\cdot6\cdot14}{2\cdot7\cdot9}\cdot a^{2-1}\cdot b^{3-2-1}\cdot c^{12-2-8}$$
   $$=2ac^2.$$
3. $$\left(\frac{5a^3}{b^4}\right)^4\cdot\frac{b^{18}}{50a^{16}}$$
   $$=\frac{5^4a^{12}}{b^{16}}\cdot\frac{b^{18}}{50a^{16}}$$
   $$=\frac{5^4}{50}\cdot a^{12-16}\cdot b^{18-16}$$
   $$=\frac{25b^2}{2a^4}.$$
4. $$\left(\frac{3x^7}{y^{10}}\right)^4:\left(\frac{3x^6}{y^8}\right)^3$$
   $$=\frac{3^4x^{28}}{y^{40}}:\frac{3^3x^{18}}{y^{24}}$$
   $$=\frac{3^4x^{28}}{y^{40}}\cdot\frac{y^{24}}{3^3x^{18}}$$
   $$=\frac{3x^{10}}{y^{16}}.$$

Ответ

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

1. $$\left(\frac{a^6}{b^3}\right)^{10}=\frac{a^{60}}{b^{30}}.$$
2. $$\left(\frac{-4m}{9n^3}\right)^2=\frac{16m^2}{81n^6}.$$
3. $$\left(\frac{-10c^7}{3d^5}\right)^3=-\frac{1000c^{21}}{27d^{15}}.$$
4. $$\left(\frac{2m^3n^2}{kp^8}\right)^6=\frac{64m^{18}n^{12}}{k^6p^{48}}.$$

Ответ

1) $$\frac{a^{60}}{b^{30}}$$; 2) $$\frac{16m^2}{81n^6}$$; 3) $$-\frac{1000c^{21}}{27d^{15}}$$; 4) $$\frac{64m^{18}n^{12}}{k^6p^{48}}$$.