360 Вправа 360Алгебра 8 клас Тарасенкова 2025 · § 9 · стор. 98

360. Знайдіть x. Подайте відповідь у вигляді степеня.

1) ${\displaystyle {(15\cdot 8\cdot {40}^0)}^{-12}=}$${\displaystyle x\cdot {100}^{-6}}$; ${\displaystyle {120}^{-12}=}$${\displaystyle x\cdot {10}^{-12}}$ | ${\displaystyle :{10}^{-12}}$

${\displaystyle x=}$${\displaystyle {\left(\frac{120}{10}\right)}^{-12}=}$${\displaystyle {12}^{-12}}$;

2) ${\displaystyle {(5\cdot 8)}^{-8}\cdot {\left({0,2}^{-2}\right)}^4=}$${\displaystyle x^{-1}\cdot 4^{-12}}$;

${\displaystyle {40}^{-8}\cdot {0,2}^{-8}=}$${\displaystyle {(40\cdot 0,2)}^{-8}=}$${\displaystyle 8^{-8}=}$${\displaystyle 2^{-24}}$;

${\displaystyle 4^{-12}=}$${\displaystyle 2^{-24}}$; ${\displaystyle 2^{-24}=}$${\displaystyle x^{-1}\cdot 2^{-24}}$ | ${\displaystyle :2^{-24}}$

${\displaystyle x^{-1}=}$${\displaystyle 1}$; ${\displaystyle x=}$${\displaystyle 1}$;

3) ${\displaystyle {(0,375x)}^6=}$${\displaystyle {\left(\frac{8}{3}\right)}^{-6}=}$${\displaystyle {\left(\frac{3}{8}\right)}^6}$; ${\displaystyle 0,375=}$${\displaystyle \frac{3}{8}}$;

${\displaystyle \frac{3}{8}x=}$${\displaystyle \frac{3}{8}}$ або ${\displaystyle \frac{3}{8}x=}$${\displaystyle -\frac{3}{8}}$ | ${\displaystyle :\frac{3}{8}}$

${\displaystyle x=}$${\displaystyle 1}$ або ${\displaystyle x=}$${\displaystyle -1}$;

4) ${\displaystyle {3,6}^{-10}=}$${\displaystyle x\cdot 4^{-5}\cdot 9^{-10}}$; ${\displaystyle 4^{-5}=}$${\displaystyle 2^{-10}}$; ${\displaystyle 2^{-10}\cdot 9^{-10}=}$${\displaystyle {18}^{-10}}$ | ${\displaystyle :{18}^{-10}}$

${\displaystyle x=}$${\displaystyle {\left(\frac{3,6}{18}\right)}^{-10}=}$${\displaystyle {0,2}^{-10}=}$${\displaystyle 5^{10}}$;

5) ${\displaystyle {\left(\frac{7}{6}\right)}^{-4}=}$${\displaystyle x\cdot {0,49}^{-2}}$; ${\displaystyle {0,49}^{-2}=}$${\displaystyle {\left({0,7}^2\right)}^{-2}=}$${\displaystyle {0,7}^{-4}}$ | ${\displaystyle :{0,7}^{-4}}$

${\displaystyle x=}$${\displaystyle {\left(\frac{6}{7}\right)}^4\cdot {0,7}^4=}$${\displaystyle {(\frac{6}{7}\cdot \frac{7}{10})}^4=}$${\displaystyle {0,6}^4}$;

6) ${\displaystyle x=}$${\displaystyle \frac{{25}^4\cdot {0,5}^{-4}}{{10}^{-2}\cdot 8^0}}$;

${\displaystyle x=}$${\displaystyle {(25:0,5)}^4\cdot {10}^2=}$${\displaystyle {50}^4\cdot {10}^2=}$${\displaystyle 5^8\cdot 2^4\cdot 2^2\cdot 5^2=}$${\displaystyle 2^6\cdot 5^{10}=}$${\displaystyle {(2^3\cdot 5^5)}^2=}$${\displaystyle {25000}^2}$.