351 Вправа 351Алгебра 8 клас Тарасенкова 2025 · § 9 · стор. 97

351. Знайдіть x, якщо:

1) ${\displaystyle a^5{b}^{-8}\cdot x=}$${\displaystyle a^{-1}{b}^{24}}$ | ${\displaystyle :a^5{b}^{-8}}$

${\displaystyle x=}$${\displaystyle \frac{a^{-1}{b}^{24}}{a^5{b}^{-8}}=}$${\displaystyle a^{-1-5}{b}^{24+8}=}$${\displaystyle a^{-6}{b}^{32}}$;

2) ${\displaystyle x:ab=}$${\displaystyle a^{-1}{b}^{-1}}$ | ${\displaystyle \cdot ab}$

${\displaystyle x=}$${\displaystyle a^{-1}{b}^{-1}\cdot ab=}$${\displaystyle a^0{b}^0=}$${\displaystyle 1}$;

3) ${\displaystyle x:b^{-16}=}$${\displaystyle a^{-7}{b}^{26}}$ | ${\displaystyle \cdot b^{-16}}$

${\displaystyle x=}$${\displaystyle a^{-7}{b}^{26}\cdot b^{-16}=}$${\displaystyle a^{-7}{b}^{10}}$;

4) ${\displaystyle {1,9}^{21}=}$${\displaystyle {1,9}^{\left(-3\right)\left(-x\right)}=}$${\displaystyle {1,9}^{3x}}$; ${\displaystyle 3x=}$${\displaystyle 21}$; ${\displaystyle x=}$${\displaystyle 7}$;

5) ${\displaystyle {4,5}^{-20}=}$${\displaystyle {4,5}^{-5x}}$; ${\displaystyle -5x=}$${\displaystyle -20}$; ${\displaystyle x=}$${\displaystyle 4}$.