336° Вправа 336Алгебра 8 клас Тарасенкова 2025 · § 9 · стор. 95

336. Запишіть як степінь:

${\displaystyle a^n\cdot b^n=}$${\displaystyle {\left(ab\right)}^n}$; ${\displaystyle \frac{a^n}{b^n}=}$${\displaystyle {\left(\frac{a}{b}\right)}^n}$. Показники однакові — множимо (ділимо) основи.

1) ${\displaystyle 4^{-3}\cdot 2^{-3}=}$${\displaystyle {(4\cdot 2)}^{-3}=}$${\displaystyle 8^{-3}}$;

2) ${\displaystyle 6^{-1}\cdot 3^{-1}=}$${\displaystyle {(6\cdot 3)}^{-1}=}$${\displaystyle {18}^{-1}}$;

3) ${\displaystyle 4^{-3}:2^{-3}=}$${\displaystyle {(4:2)}^{-3}=}$${\displaystyle 2^{-3}}$;

4) ${\displaystyle 6^{-1}:3^{-1}=}$${\displaystyle {(6:3)}^{-1}=}$${\displaystyle 2^{-1}}$;

5) ${\displaystyle 5^{-9}\cdot 2^{-9}\cdot 8^{-9}=}$${\displaystyle {(5\cdot 2\cdot 8)}^{-9}=}$${\displaystyle {80}^{-9}}$;

6) ${\displaystyle 1^{-4}\cdot 4^{-4}\cdot 3^{-4}=}$${\displaystyle {(1\cdot 4\cdot 3)}^{-4}=}$${\displaystyle {12}^{-4}}$;

7) ${\displaystyle b^{-12}\cdot a^{-12}=}$${\displaystyle {\left(ba\right)}^{-12}}$;

8) ${\displaystyle x^{-5}:y^{-5}=}$${\displaystyle {\left(\frac{x}{y}\right)}^{-5}}$;

9) ${\displaystyle \frac{m^{-5}}{n^{-5}}=}$${\displaystyle {\left(\frac{m}{n}\right)}^{-5}}$;

10) ${\displaystyle p^{-6}\cdot m^{-6}\cdot n^{-6}=}$${\displaystyle {\left(pmn\right)}^{-6}}$;

11) ${\displaystyle a^{-1}\cdot b^{-1}\cdot c^{-1}=}$${\displaystyle {\left(abc\right)}^{-1}}$;

12) ${\displaystyle 3^{-4}\cdot m^{-4}\cdot n^{-4}=}$${\displaystyle {\left(3mn\right)}^{-4}}$;

13) ${\displaystyle \frac{x^{-5}{y}^{-5}}{z^{-5}}=}$${\displaystyle {\left(\frac{xy}{z}\right)}^{-5}}$;

14) ${\displaystyle \frac{3^{-1}}{a^{-1}{b}^{-1}}=}$${\displaystyle {\left(\frac{3}{ab}\right)}^{-1}}$;

15) ${\displaystyle \frac{x^{-2}{y}^{-2}}{z^{-2}{h}^{-2}}=}$${\displaystyle {\left(\frac{xy}{zh}\right)}^{-2}}$;

16) ${\displaystyle \frac{d^{-10}{b}^{-10}}{a^{-10}{c}^{-10}}=}$${\displaystyle {\left(\frac{db}{ac}\right)}^{-10}}$.