378° Вправа 378Алгебра 8 клас Тарасенкова 2025 · § 10 · стор. 106

378. Запишіть як степінь з натуральним показником:

${\displaystyle {\left(\frac{A}{B}\right)}^{-n}=}$${\displaystyle {\left(\frac{B}{A}\right)}^n}$; ${\displaystyle A^{-n}=}$${\displaystyle \frac{1}{A^n}}$.

1) ${\displaystyle {(x-y)}^{-2}=}$${\displaystyle \frac{1}{{\left(x-y\right)}^2}}$;

2) ${\displaystyle {(10+m)}^{-4}=}$${\displaystyle \frac{1}{{\left(10+m\right)}^4}}$;

3) ${\displaystyle {(x^2-1)}^{-6}=}$${\displaystyle \frac{1}{{\left(x^2-1\right)}^6}}$;

4) ${\displaystyle {(a-c)}^{-8}=}$${\displaystyle \frac{1}{{\left(a-c\right)}^8}}$;

5) ${\displaystyle {\left(\frac{1}{x}\right)}^{-5}=}$${\displaystyle x^5}$;

6) ${\displaystyle {\left(\frac{1}{b}\right)}^{-4}=}$${\displaystyle b^4}$;

7) ${\displaystyle {\left(\frac{a}{b}\right)}^{-2}=}$${\displaystyle {\left(\frac{b}{a}\right)}^2}$;

8) ${\displaystyle {(-\frac{a}{b})}^{-2}=}$${\displaystyle {(-\frac{b}{a})}^2=}$${\displaystyle {\left(\frac{b}{a}\right)}^2}$;

9) ${\displaystyle {\left(\frac{m}{n}\right)}^{-6}=}$${\displaystyle {\left(\frac{n}{m}\right)}^6}$;

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

11) ${\displaystyle {(-\frac{p}{n})}^{-10}=}$${\displaystyle {\left(\frac{n}{p}\right)}^{10}}$;

12) ${\displaystyle {(-\frac{3}{z})}^{-3}=}$${\displaystyle {\left(-\frac{z}{3}\right)}^3}$.