325° Вправа 325Алгебра 8 клас Тарасенкова 2025 · § 9 · стор. 94

325. Обчисліть:

${\displaystyle \frac{a^n}{a^m}=}$${\displaystyle a^{n-m}}$ — від показника чисельника віднімаємо показник знаменника.

1) ${\displaystyle \frac{4^2}{4^{-1}}=}$${\displaystyle 4^{2-\left(-1\right)}=}$${\displaystyle 4^3=}$${\displaystyle 64}$;

2) ${\displaystyle \frac{4^{-2}}{4^{-3}}=}$${\displaystyle 4^{-2-\left(-3\right)}=}$${\displaystyle 4}$;

3) ${\displaystyle \frac{4^{-1}}{4^3}=}$${\displaystyle 4^{-1-3}=}$${\displaystyle 4^{-4}=}$${\displaystyle \frac{1}{256}}$;

4) ${\displaystyle \frac{4^2}{4^3}=}$${\displaystyle 4^{2-3}=}$${\displaystyle 4^{-1}=}$${\displaystyle \frac{1}{4}}$;

5) ${\displaystyle \frac{4^2}{4^{-2}}=}$${\displaystyle 4^{2-\left(-2\right)}=}$${\displaystyle 4^4=}$${\displaystyle 256}$;

6) ${\displaystyle \frac{4^{-2}}{4^2}=}$${\displaystyle 4^{-2-2}=}$${\displaystyle 4^{-4}=}$${\displaystyle \frac{1}{256}}$;

7) ${\displaystyle \frac{4^{-2}}{4^{-2}}=}$${\displaystyle 4^{-2-\left(-2\right)}=}$${\displaystyle 4^0=}$${\displaystyle 1}$;

8) ${\displaystyle \frac{4}{4^{-2}}=}$${\displaystyle 4^{1-\left(-2\right)}=}$${\displaystyle 4^3=}$${\displaystyle 64}$;

9) ${\displaystyle \frac{4^{-5}}{4^{-8}}=}$${\displaystyle 4^{-5-\left(-8\right)}=}$${\displaystyle 4^3=}$${\displaystyle 64}$;

10) ${\displaystyle \frac{4^2}{4^0}=}$${\displaystyle 4^{2-0}=}$${\displaystyle 16}$.