251 Вправа 251Алгебра 8 клас Бевз 2025 · § 5 · стор. 53

251. Піднеси до степеня дріб.

а) ${\displaystyle {(-\frac{x^{2}z}{a^{3}n})}^2=}$${\displaystyle \frac{{\left(x^{2}z\right)}^2}{{\left(a^{3}n\right)}^2}=}$${\displaystyle \frac{x^4{z}^2}{a^6{n}^2}}$;

б) ${\displaystyle {\left(\frac{-3m^{2}n}{2a{c}^3}\right)}^3=}$${\displaystyle \frac{{(-3m^{2}n)}^3}{{\left(2a{c}^3\right)}^3}=}$${\displaystyle -\frac{27m^6{n}^3}{8a^3{c}^9}}$;

в) ${\displaystyle {\left(\frac{x{y}^{2}z}{-2a{n}^4}\right)}^4=}$${\displaystyle \frac{{\left(x{y}^{2}z\right)}^4}{{(-2a{n}^4)}^4}=}$${\displaystyle \frac{x^4{y}^8{z}^4}{16a^4{n}^{16}}}$.