Решебник по алгебре 7 класс Мерзляк Задание 223

\[\boxed{\text{223\ (223).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ a^{4} \cdot a^{3} = a^{7}\]

\[a^{4} \cdot a^{3} \neq a^{12}.\]

\[2)\ a \cdot a = a^{2}\]

\[a \cdot a \neq 2a.\]

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

\[\left( a^{3} \right)^{2} = a^{9}.\]

\[4)\ 3^{2} \cdot 5^{2} = (3 \cdot 5)^{2} = 15^{2}\]

\[3^{2} \cdot 5^{2} \neq 15^{4}.\]

\[5)\ 2^{2} \cdot 7^{3} = 2^{2} \cdot 7^{2} \cdot 7 =\]

\[= (2 \cdot 7)^{2} \cdot 7 = 14^{2} \cdot 7\]

\[2^{2} \cdot 7^{3} \neq 14^{5}.\]

\[6)\ (2a)^{4} = 2^{4} \cdot a^{4} = 16a^{4}\]

\[\ (2a)^{4} \neq 8a^{4}.\]

\[7)\ 3 \cdot 4^{3} = 3 \cdot 4 \cdot 4^{2} = 12 \cdot 16\]

\[3 \cdot 4^{3} \neq 12^{3}.\]

\[8)\ a^{7} \cdot b^{7} = \left( \text{ab} \right)^{7}\]

\[a^{7} \cdot b^{7} \neq \left( \text{ab} \right)^{14}.\]

\[9)\ a^{3} \cdot b^{2} = a \cdot a^{2} \cdot b^{2} =\]

\[= \left( \text{ab} \right)^{2} \cdot a\]

\[a^{3} \cdot b^{2} \neq \left( \text{ab} \right)^{6}.\]