Решебник по алгебре 7 класс Мерзляк ФГОС Задание 285

 

\[\boxed{\text{285\ (285).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[2a^{2}b = 7;\ \ a^{3}c^{2} = 2;\ \ a^{2}b = \frac{7}{2}\]

\[1)\ 6a^{5}bc^{2} = 3 \cdot 2a^{2}b \cdot a^{3}c^{2} =\]

\[= 3 \cdot 7 \cdot 2 = 42\]

\[2)\ a^{7}b^{2}c^{2} = a^{3}c^{2} \cdot a^{4}b^{2} =\]

\[= a^{3}c^{2} \cdot \left( a^{2}b \right)^{2} = \left( \frac{7}{2} \right)^{2} \cdot 2 =\]

\[= \frac{49}{4} \cdot 2 = \frac{49}{2} = 24,5\]

\[3)\ 2\frac{1}{7}a^{8}bc^{4} =\]

\[= \frac{15}{7} \cdot a^{2}b \cdot \left( a^{3}c^{2} \right)^{2} =\]

\[= \frac{15}{7} \cdot \frac{7}{2} \cdot 2^{2} = 15 \cdot 2 = 30\]

\[\boxed{\text{285.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[Представим\ степени\ в\ виде\ \]

\[произведения\ \ множителей,\ \]

\[найдем\ и\ сравним\ полученные\ \]

\[значения.\]

\[1)\ 2^{2} \cdot 2^{3} = 2^{5}\]

\[2^{2} \cdot 2^{3} = \ 4 \cdot 8 = 32\]

\[2^{5} = 32.\]

\[2)\ 4^{2} \cdot 4^{1} = 4^{3}\]

\[4^{2} \cdot 4^{1} = 16 \cdot 4 = 64\]

\[4^{3} = 64.\]

\[3)\ \left( 3^{3} \right)^{2} = 3^{6}\]

\[\left( 3^{3} \right)^{2} = (27)^{2} = 729\]

\[3^{6} = 9 \cdot 9 \cdot 9 = 81 \cdot 9 =\]

\[= 729.\]

\[4)\ \left( \left( \frac{1}{2} \right)^{4} \right)^{3} = \left( \frac{1}{2} \right)^{12}\]

\[\left( \left( \frac{1}{2} \right)^{4} \right)^{3} = \left( \frac{1}{16} \right)^{3} =\]

\[= \frac{1}{16 \cdot 16 \cdot 16} = \frac{1}{256 \cdot 16}\]

\[\left( \frac{1}{2} \right)^{12} = \frac{1}{4096}\]

\[2^{10} = 1024\]

\[2^{12} = 1024 \cdot 4 = 4096.\]

\[5)\ 5^{3} \cdot 2^{3} = (5 \cdot 2)^{3}\]

\[5^{3} \cdot 2^{3} = 125 \cdot 8 = 1000\]

\[(5 \cdot 2)^{3} = 10^{3} = 1000.\]

\[6)\ (0,25 \cdot 4)^{2} = {0,25}^{2} \cdot 4^{2}\]

\[(0,25 \cdot 4)^{2} = 1^{2} = 1\]

\[{0,25}^{2} \cdot 4^{2} = 0,0625 \cdot 16 = 1.\]