352 Вправа 352Алгебра 8 клас Тарасенкова 2025 · § 9 · стор. 97

352. Знайдіть x, якщо:

1) ${\displaystyle a^{-14}b\cdot x=}$${\displaystyle a^2{b}^{-14}}$ | ${\displaystyle :a^{-14}b}$

${\displaystyle x=}$${\displaystyle \frac{a^2{b}^{-14}}{a^{-14}b}=}$${\displaystyle a^{2+14}{b}^{-14-1}=}$${\displaystyle a^{16}{b}^{-15}}$;

2) ${\displaystyle a^{-100}{b}^{100}:x=}$${\displaystyle b^{-50}}$, тобто ${\displaystyle x=}$${\displaystyle a^{-100}{b}^{100}:b^{-50}}$:

${\displaystyle x=}$${\displaystyle a^{-100}{b}^{100+50}=}$${\displaystyle a^{-100}{b}^{150}}$;

3) ${\displaystyle 3^{-36}=}$${\displaystyle 3^{-9x}}$; ${\displaystyle -9x=}$${\displaystyle -36}$; ${\displaystyle x=}$${\displaystyle 4}$;

4) ${\displaystyle 6^{-14}=}$${\displaystyle 6^{2x}}$; ${\displaystyle 2x=}$${\displaystyle -14}$; ${\displaystyle x=}$${\displaystyle -7}$.