221 Вправа 221Алгебра 8 клас Бевз 2025 · § 5 · стор. 50

221. Піднеси до квадрата і куба дріб.

а) квадрат: ${\displaystyle {\left(\frac{2}{3}\right)}^2=}$${\displaystyle \frac{2^2}{3^2}=}$${\displaystyle \frac{4}{9}}$;

куб: ${\displaystyle {\left(\frac{2}{3}\right)}^3=}$${\displaystyle \frac{2^3}{3^3}=}$${\displaystyle \frac{8}{27}}$;

б) квадрат: ${\displaystyle {\left(\frac{x}{ac}\right)}^2=}$${\displaystyle \frac{x^2}{{\left(ac\right)}^2}=}$${\displaystyle \frac{x^2}{a^2{c}^2}}$;

куб: ${\displaystyle {\left(\frac{x}{ac}\right)}^3=}$${\displaystyle \frac{x^3}{{\left(ac\right)}^3}=}$${\displaystyle \frac{x^3}{a^3{c}^3}}$;

в) квадрат: ${\displaystyle {\left(\frac{1}{2x^2}\right)}^2=}$${\displaystyle \frac{1^2}{{\left(2x^2\right)}^2}=}$${\displaystyle \frac{1}{4x^4}}$;

куб: ${\displaystyle {\left(\frac{1}{2x^2}\right)}^3=}$${\displaystyle \frac{1^3}{{\left(2x^2\right)}^3}=}$${\displaystyle \frac{1}{8x^6}}$;

г) квадрат: ${\displaystyle {\left(\frac{-2a}{x^3}\right)}^2=}$${\displaystyle \frac{{(-2a)}^2}{{\left(x^3\right)}^2}=}$${\displaystyle \frac{4a^2}{x^6}}$;

куб: ${\displaystyle {\left(\frac{-2a}{x^3}\right)}^3=}$${\displaystyle \frac{{(-2a)}^3}{{\left(x^3\right)}^3}=}$${\displaystyle -\frac{8a^3}{x^9}}$.