451 Вправа 451Алгебра 8 клас Бевз 2025 · § 9 · стор. 91

451. Подай степінь у вигляді добутку.

а) ${\displaystyle {\left(0,5x^{-3}{y}^2\right)}^{-2}}$=

=${\displaystyle {\left(0,5\right)}^{-2}\cdot x^{\left(-3\right)\cdot \left(-2\right)}\cdot y^{2\cdot \left(-2\right)}=}$${\displaystyle 4x^6{y}^{-4}}$;

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

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

в) ${\displaystyle {(-0,2m^2{n}^{-4})}^{-3}}$=

=${\displaystyle {\left(-0,2\right)}^{-3}\cdot m^{2\cdot \left(-3\right)}\cdot n^{\left(-4\right)\cdot \left(-3\right)}}$=

=${\displaystyle -125m^{-6}{n}^{12}}$;

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

=${\displaystyle {\left(\frac{1}{2}\right)}^{-3}\cdot x^{3\cdot \left(-3\right)}\cdot y^{\left(-2\right)\cdot \left(-3\right)}=}$${\displaystyle 8x^{-9}{y}^6}$;

ґ) ${\displaystyle {\left(\frac{5}{6}{m}^{-8}n\right)}^{-1}}$=

=${\displaystyle {\left(\frac{5}{6}\right)}^{-1}\cdot m^{\left(-8\right)\cdot \left(-1\right)}\cdot n^{1\cdot \left(-1\right)}=}$${\displaystyle 1,2m^8{n}^{-1}}$;

д) ${\displaystyle {(-0,3x^{-3}y)}^2}$=

=${\displaystyle {\left(-0,3\right)}^2\cdot x^{\left(-3\right)\cdot 2}\cdot y^{1\cdot 2}=}$${\displaystyle 0,09x^{-6}{y}^2}$.