Решебник по алгебре 8 класс Мерзляк ФГОС Задание 154

 

\[\boxed{\text{154\ (154).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ \left( \frac{a^{6}}{b^{3}} \right)^{10} = \frac{a^{60}}{b^{30}}.\]

\[2)\ \left( - \frac{4m}{9n^{3}} \right)^{2} = \frac{16m^{2}}{81n^{6}}.\]

\[3)\ \left( - \frac{10c^{7}}{3d^{5}} \right)^{3} = - \frac{1000c^{21}}{27d^{15}}.\]

\[4)\ \left( \frac{2m^{3}n^{2}}{kp^{8}} \right)^{6} = \frac{64m^{18}n^{12}}{k^{6}p^{48}}\text{.\ }\]

\[\boxed{\text{154.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\frac{3a^{4}b^{3}}{10c^{5}} \cdot \frac{4b^{4}c^{2}}{27a^{7}}\ :\frac{5b^{7}}{9a^{3}c^{3}} =\]

\[= \frac{3a^{4}b^{3} \cdot 4b^{4}c^{2} \cdot 9a^{3}c^{3}}{10c^{5} \cdot 27a^{7} \cdot 5b^{7}} = \frac{2}{25}\]

\[2)\frac{3a^{2}}{2b^{2}c^{2}}\ :\frac{7c^{8}}{6b^{3}}\ :\frac{9ab}{14c^{12}} =\]

\[= \frac{3a^{2} \cdot 6b^{3} \cdot 14c^{12}}{2b^{2}c^{2} \cdot 7c^{8} \cdot 9ab} = \frac{2ac^{2}}{1} =\]

\[= 2ac^{2}\]

\[3)\ \left( \frac{5a^{3}}{b^{4}} \right)^{4} \cdot \frac{b^{18}}{50a^{16}} =\]

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

\[4)\ \left( \frac{3x^{7}}{y^{10}} \right)^{4}:\left( \frac{3x^{6}}{y^{8}} \right)^{3} =\]

\[= \frac{3^{4} \cdot x^{28} \cdot y^{24}}{y^{40} \cdot 3^{3} \cdot x^{18}} = \frac{3x^{10}}{y^{16}}\]