341° Вправа 341Алгебра 8 клас Тарасенкова 2025 · § 9 · стор. 96

341. Знайдіть x:

1) ${\displaystyle {(4\cdot 5)}^{-3}=}$${\displaystyle x\cdot 5^{-3}}$; ${\displaystyle 4^{-3}\cdot 5^{-3}=}$${\displaystyle x\cdot 5^{-3}}$; ${\displaystyle x=}$${\displaystyle 4^{-3}=}$${\displaystyle \frac{1}{64}}$;

2) ${\displaystyle {(2\cdot 15)}^{-6}=}$${\displaystyle {15}^{-6}\cdot x}$; ${\displaystyle 2^{-6}\cdot {15}^{-6}=}$${\displaystyle {15}^{-6}\cdot x}$; ${\displaystyle x=}$${\displaystyle 2^{-6}=}$${\displaystyle \frac{1}{64}}$;

3) ${\displaystyle {(2\cdot 3\cdot 4)}^{-2}=}$${\displaystyle x\cdot 2^{-2}\cdot 4^{-2}}$;

${\displaystyle 2^{-2}\cdot 3^{-2}\cdot 4^{-2}=}$${\displaystyle x\cdot 2^{-2}\cdot 4^{-2}}$; ${\displaystyle x=}$${\displaystyle 3^{-2}=}$${\displaystyle \frac{1}{9}}$;

4) ${\displaystyle {\left(\frac{3}{8}\right)}^{-6}=}$${\displaystyle \frac{x^{-6}}{8^{-6}}}$; ${\displaystyle \frac{3^{-6}}{8^{-6}}=}$${\displaystyle \frac{x^{-6}}{8^{-6}}}$; ${\displaystyle x^{-6}=}$${\displaystyle 3^{-6}}$; ${\displaystyle x=}$${\displaystyle 3}$ (або ${\displaystyle x=}$${\displaystyle -3}$).