Задание 10 Параграф 5 ГДЗ Рабочая тетрадь 1 Мерзляк Полонский 8 класс (Алгебра)

1) (5a^3)/(2b^3 c^3 )•(6b^4)/(11c^6 ) :15ab/(44c^8 );
2) (35m^2 n)/p^2 :(7mn^5)/(6p^5 ) :(4n^4)/m^3 ;
3) (-(3x^4 y^3)/(2z^8 ))^3 :(-(3x^5 y^2)/(2z^4 ))^4;
4) ((7a^6)/b^9 )^5 :((7a^10)/b^16 )^3.

1. $$\frac{5a^3}{2b^3c^3}\cdot\frac{6b^4}{11c^6}:\frac{15ab}{44c^8}= \frac{5a^3}{2b^3c^3}\cdot\frac{6b^4}{11c^6}\cdot\frac{44c^8}{15ab}$$
   $$=\frac{5\cdot 6\cdot 44\cdot a^3b^4c^8}{2\cdot 11\cdot 15\cdot ab^3c^9} =\frac{4a^2b}{c}$$
2. $$\frac{35m^2n}{p^2}:\frac{7mn^5}{6p^5}:\frac{4n^4}{m^3} =\frac{35m^2n}{p^2}\cdot\frac{6p^5}{7mn^5}\cdot\frac{m^3}{4n^4}$$
   $$=\frac{35\cdot 6}{7\cdot 4}\cdot\frac{m^2\cdot m^3}{m}\cdot\frac{p^5}{p^2}\cdot\frac{n}{n^5\cdot n^4} =\frac{15m^4p^3}{2n^8}$$
3. $$\left(-\frac{3x^4y^3}{2z^8}\right)^3:\left(-\frac{3x^5y^2}{2z^4}\right)^4 =-\frac{3^3x^{12}y^9}{2^3z^{24}}:\frac{3^4x^{20}y^8}{2^4z^{16}}$$
   $$=-\frac{3^3x^{12}y^9}{2^3z^{24}}\cdot\frac{2^4z^{16}}{3^4x^{20}y^8} =-\frac{2y}{3x^8z^8}$$
4. $$\left(\frac{7a^6}{b^9}\right)^5:\left(\frac{7a^{10}}{b^{16}}\right)^3 =\frac{7^5a^{30}}{b^{45}}:\frac{7^3a^{30}}{b^{48}}$$
   $$=\frac{7^5a^{30}}{b^{45}}\cdot\frac{b^{48}}{7^3a^{30}} =49b^3$$

Ответ

1) $$\frac{4a^2b}{c}$$; 2) $$\frac{15m^4p^3}{2n^8}$$; 3) $$-\frac{2y}{3x^8z^8}$$; 4) $$49b^3$$.