Упр.31 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (21b^8)/(10c^6 ) :(7b^2)/(30c^3);
2) (40a^5 b^9)/(39c^6 d^14 ) :(-(5a^8 b^3)/(26c^12 d^7 ));
3) 36x^16 y^14 :(18x^18 y^10)/(11m^3);
4) (60m^6 n^5)/(17p^4 ) :(15m^8 n^10);
5) (17a^6 b^10)/(16c^2 d^5 ) :(34a^4 b^4)/(24c^6 d^6 ) :(15b^8 d^4)/(8a^8 c^3);
6) (-(9x^5 y^2)/(7z^4 ))^3 :(-(9x^4 y^10)/(7z^3 ))^4.

1. $$\frac{21b^8}{10c^6}:\frac{7b^2}{30c^3}=\frac{21b^8}{10c^6}\cdot\frac{30c^3}{7b^2}$$
   $$=\frac{21\cdot 30}{10\cdot 7}\cdot b^{8-2}\cdot c^{3-6}=9b^6\cdot \frac{1}{c^3}$$
   $$=\frac{9b^6}{c^3}$$

2. $$\frac{40a^5b^9}{39c^6d^{14}}:\left(-\frac{5a^8b^3}{26c^{12}d^7}\right)=\frac{40a^5b^9}{39c^6d^{14}}\cdot\frac{26c^{12}d^7}{-5a^8b^3}$$
   $$=-\frac{40\cdot 26}{39\cdot 5}\cdot a^{5-8}\cdot b^{9-3}\cdot c^{12-6}\cdot d^{7-14}$$
   $$=-\frac{16b^6c^6}{3a^3d^7}$$

3. $$36x^{16}y^{14}:\frac{18x^{18}y^{10}}{11m^3}=36x^{16}y^{14}\cdot\frac{11m^3}{18x^{18}y^{10}}$$
   $$=2\cdot 11\cdot m^3\cdot x^{16-18}\cdot y^{14-10}$$
   $$=\frac{22m^3y^4}{x^2}$$

4. $$\frac{60m^6n^5}{17p^4}:(15m^8n^{10})=\frac{60m^6n^5}{17p^4}\cdot\frac{1}{15m^8n^{10}}$$
   $$=\frac{60}{17\cdot 15}\cdot \frac{1}{m^2n^5p^4}=\frac{4}{17m^2n^5p^4}$$

5. $$\frac{17a^6b^{10}}{16c^2d^5}:\frac{34a^4b^4}{24c^6d^6}:\frac{15b^8d^4}{8a^8c^3}$$
   $$=\frac{17a^6b^{10}}{16c^2d^5}\cdot\frac{24c^6d^6}{34a^4b^4}\cdot\frac{8a^8c^3}{15b^8d^4}$$
   $$=\frac{17\cdot 24\cdot 8}{16\cdot 34\cdot 15}\cdot a^{6-4+8}\cdot b^{10-4-8}\cdot c^{6-2+3}\cdot d^{6-5-4}$$
   $$=\frac{2a^{10}c^7}{5b^2d^3}$$

6. $$\left(-\frac{9x^5y^2}{7z^4}\right)^3:\left(-\frac{9x^4y^{10}}{7z^3}\right)^4$$
   $$=-\frac{9^3x^{15}y^6}{7^3z^{12}}:\frac{9^4x^{16}y^{40}}{7^4z^{12}}$$
   $$=-\frac{9^3x^{15}y^6}{7^3z^{12}}\cdot\frac{7^4z^{12}}{9^4x^{16}y^{40}}$$
   $$=-\frac{7}{9xy^{34}}$$

Ответ

$$1)\ \frac{9b^6}{c^3};\quad 2)\ -\frac{16b^6c^6}{3a^3d^7};\quad 3)\ \frac{22m^3y^4}{x^2};\quad 4)\ \frac{4}{17m^2n^5p^4};\quad 5)\ \frac{2a^{10}c^7}{5b^2d^3};\quad 6)\ -\frac{7}{9xy^{34}}.$$