Решебник по алгебре 7 класс Мерзляк Задание 271

\[\boxed{\text{271\ (}\text{н}\text{).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \left( 3a^{2}b \right)^{2} = 3^{2} \cdot \left( a^{2} \right)^{2} \cdot b^{2} =\]

\[= 9a^{4}b^{2}\]

\[2)\ \left( 16x^{6}y^{7}z^{8} \right)^{2} =\]

\[= 16^{2} \cdot \left( x^{6} \right)^{2} \cdot \left( y^{7} \right)^{2} \cdot \left( z^{8} \right)^{2} =\]

\[= 256x^{12}y^{14}z^{16}\]

\[3)\ \left( - \frac{1}{5}c^{6}d \right)^{4} =\]

\[= \left( - \frac{1}{5} \right)^{4} \cdot \left( c^{6} \right)^{4} \cdot d^{4} =\]

\[= \frac{1}{625}c^{24}d^{4}\]

\[\boxed{\text{271\ (}\text{с}\text{).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \left( 3a^{2}b \right)^{2} = 3^{2} \cdot \left( a^{2} \right)^{2} \cdot b^{2} =\]

\[= 9a^{4}b^{2}\]

\[2)\ \left( - 0,2x^{3}y^{4} \right)^{3} =\]

\[= ( - 0,2)^{3} \cdot \left( x^{3} \right)^{3} \cdot \left( y^{4} \right)^{3} =\]

\[= - 0,008x^{9}y^{12}\]

\[3)\ \left( - 10m^{2}y^{8} \right)^{5} =\]

\[= ( - 10)^{5} \cdot \left( m^{2} \right)^{5} \cdot \left( y^{8} \right)^{5} =\]

\[= - 100\ 000m^{10}y^{40}\]

\[4)\ \left( 16x^{6}y^{7}z^{8} \right)^{2} =\]

\[= 16^{2} \cdot \left( x^{6} \right)^{2} \cdot \left( y^{7} \right)^{2} \cdot \left( z^{8} \right)^{2} =\]

\[= 256x^{12}y^{14}z^{16}\]

\[5)\ \left( - \frac{1}{5}c^{6}d \right)^{4} =\]

\[= \left( - \frac{1}{5} \right)^{4} \cdot \left( c^{6} \right)^{4} \cdot d^{4} =\]

\[= \frac{1}{625}c^{24}d^{4}\]

\[6)\ \left( 1\frac{1}{2}a^{8}b^{9} \right)^{6} =\]

\[= \left( \frac{3}{2} \right)^{6} \cdot \left( a^{8} \right)^{6} \cdot \left( b^{9} \right)^{6} =\]

\[= \frac{729}{64}a^{48}b^{54} = 11\frac{25}{64}a^{48}b^{54}\]