340° Вправа 340Алгебра 8 клас Тарасенкова 2025 · § 9 · стор. 96

340. Знайдіть x:

Розкладаємо ліву частину за властивістю ${\displaystyle {\left(ab\right)}^n=}$${\displaystyle a^n\cdot b^n}$ і порівнюємо.

1) ${\displaystyle {(-2\cdot 9)}^{-4}=}$${\displaystyle x\cdot 9^{-4}}$; ${\displaystyle {(-2)}^{-4}\cdot 9^{-4}=}$${\displaystyle x\cdot 9^{-4}}$; ${\displaystyle x=}$${\displaystyle {(-2)}^{-4}=}$${\displaystyle \frac{1}{16}}$. ${\displaystyle x=}$${\displaystyle \frac{1}{16}}$;

2) ${\displaystyle {(7\cdot 10)}^{-3}=}$${\displaystyle 7^{-3}\cdot x}$; ${\displaystyle 7^{-3}\cdot {10}^{-3}=}$${\displaystyle 7^{-3}\cdot x}$; ${\displaystyle x=}$${\displaystyle {10}^{-3}=}$${\displaystyle 0,001}$;

3) ${\displaystyle {(5\cdot 8\cdot 12)}^{-1}=}$${\displaystyle x\cdot 8^{-1}\cdot {12}^{-1}}$;

${\displaystyle 5^{-1}\cdot 8^{-1}\cdot {12}^{-1}=}$${\displaystyle x\cdot 8^{-1}\cdot {12}^{-1}}$; ${\displaystyle x=}$${\displaystyle 5^{-1}=}$${\displaystyle \frac{1}{5}}$;

4) ${\displaystyle {\left(\frac{2}{5}\right)}^{-4}=}$${\displaystyle \frac{2^{-4}}{x^{-4}}}$; ${\displaystyle \frac{2^{-4}}{5^{-4}}=}$${\displaystyle \frac{2^{-4}}{x^{-4}}}$; ${\displaystyle x^{-4}=}$${\displaystyle 5^{-4}}$; ${\displaystyle x=}$${\displaystyle 5}$ (або ${\displaystyle x=}$${\displaystyle -5}$, бо показник парний);

5) ${\displaystyle {\left(\frac{1}{7}\right)}^{-9}=}$${\displaystyle \frac{1}{x^{-9}}}$; ${\displaystyle {\left(\frac{1}{7}\right)}^{-9}=}$${\displaystyle 7^9}$; ${\displaystyle \frac{1}{x^{-9}}=}$${\displaystyle x^9}$; ${\displaystyle x^9=}$${\displaystyle 7^9}$; ${\displaystyle x=}$${\displaystyle 7}$;

6) ${\displaystyle {\left(1\frac{1}{3}\right)}^{-7}=}$${\displaystyle \frac{x^{-7}}{3^{-7}}}$;

${\displaystyle {\left(\frac{4}{3}\right)}^{-7}=}$${\displaystyle \frac{4^{-7}}{3^{-7}}=}$${\displaystyle \frac{x^{-7}}{3^{-7}}}$; ${\displaystyle x^{-7}=}$${\displaystyle 4^{-7}}$; ${\displaystyle x=}$${\displaystyle 4}$.