388° Вправа 388Алгебра 8 клас Тарасенкова 2025 · § 10 · стор. 108

388. Піднесіть до степеня вираз:

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

1) ${\displaystyle {\left(2x^{-3}y\right)}^{-4}=}$${\displaystyle 2^{-4}{x}^{\left(-3\right)\left(-4\right)}{y}^{-4}=}$${\displaystyle \frac{x^{12}}{16y^4}}$;

2) ${\displaystyle {\left(x^{-6}{y}^{-4}\right)}^{-5}=}$${\displaystyle x^{\left(-6\right)\left(-5\right)}{y}^{\left(-4\right)\left(-5\right)}=}$${\displaystyle x^{30}{y}^{20}}$;

3) ${\displaystyle {(0,5x^{-12}{y}^4)}^{-1}=}$${\displaystyle {0,5}^{-1}{x}^{12}{y}^{-4}=}$${\displaystyle \frac{2x^{12}}{y^4}}$;

4) ${\displaystyle {\left(\frac{x^2}{y}\right)}^{-5}=}$${\displaystyle {\left(\frac{y}{x^2}\right)}^5=}$${\displaystyle \frac{y^5}{x^{10}}}$;

5) ${\displaystyle {\left(\frac{3}{y}\right)}^{-3}=}$${\displaystyle {\left(\frac{y}{3}\right)}^3=}$${\displaystyle \frac{y^3}{27}}$;

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

7) ${\displaystyle {\left(\frac{a^{-2}}{4b^4}\right)}^{-3}=}$${\displaystyle {\left(\frac{4b^4}{a^{-2}}\right)}^3=}$${\displaystyle \frac{64b^{12}}{a^{-6}}=}$${\displaystyle 64a^6{b}^{12}}$;

8) ${\displaystyle {(-\frac{x^{-3}}{2y^{-5}})}^2=}$${\displaystyle \frac{x^{-6}}{4y^{-10}}=}$${\displaystyle \frac{y^{10}}{4x^6}}$;

9) ${\displaystyle {(-\frac{3a^{-5}}{b^4})}^{-1}=}$${\displaystyle -\frac{b^4}{3a^{-5}}=}$${\displaystyle -\frac{a^5{b}^4}{3}}$.