Решебник по алгебре 8 класс Мерзляк Задание 155

\[\boxed{\text{155\ (155).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\frac{6a^{4}b^{2}}{35c^{3}} \cdot \frac{14b^{2}}{a^{7}c^{5}} \cdot \frac{5a^{3}c^{8}}{18b^{4}} =\]

\[= \frac{6a^{4}b^{2} \cdot 14b^{2} \cdot 5a^{3}c^{8}}{35c^{3} \cdot a^{7}c^{5} \cdot 18b^{4}} = \frac{2}{3}\]

\[2)\frac{33m^{8}}{34n^{8}}\ :\frac{88m^{4}}{51n^{4}}\ :\frac{21m^{6}}{16n^{2}} =\]

\[= \frac{33m^{8} \cdot 51n^{4} \cdot 16n^{2}}{34n^{8} \cdot 88m^{4} \cdot 21m^{6}} = \frac{3}{7n^{2}m^{2}}\]

\[3)\frac{36x^{6}}{49y^{5}}\ :\frac{24x^{9}}{25y^{4}} \cdot \frac{7x^{2}}{30y} =\]

\[= \frac{36x^{6} \cdot 25y^{4} \cdot 7x^{2}}{49y^{5} \cdot 24x^{9} \cdot 30y} = \frac{5}{28xy^{2}}\]

\[4)\ \left( \frac{m^{5}n}{3p^{3}} \right)^{3}:\frac{m^{10}n^{5}}{54p^{8}} =\]

\[= \frac{m^{15}n^{3} \cdot 54p^{8}}{27p^{9} \cdot m^{10}n^{5}} = \frac{2m^{5}}{pn^{2}}\]

\[5)\ \left( \frac{2a^{5}}{y^{6}} \right)^{4}:\left( \frac{4a^{6}}{y^{8}} \right)^{3} =\]

\[= \frac{16a^{20} \cdot y^{24}}{y^{24} \cdot 64a^{18}} = \frac{a^{2}}{4}\]

\[6)\ \left( - \frac{27x^{3}}{16y^{5}} \right)^{2} \cdot \left( \frac{8y^{3}}{9x^{2}} \right)^{3} =\]

\[= \frac{27 \cdot 27 \cdot x^{6} \cdot 64 \cdot 8 \cdot y^{9}}{16 \cdot 16 \cdot y^{10} \cdot 81 \cdot 9 \cdot x^{6}} = \frac{2}{y}\]