452 Вправа 452Алгебра 8 клас Бевз 2025 · § 9 · стор. 91

452. Подай степінь у вигляді добутку.

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

б) ${\displaystyle {\left(a^3{y}^{-2}\right)}^4=}$${\displaystyle a^{3\cdot 4}\cdot y^{\left(-2\right)\cdot 4}=}$${\displaystyle a^{12}{y}^{-8}}$;

в) ${\displaystyle {\left(5a^{-3}b\right)}^{-1}}$=

=${\displaystyle 5^{-1}\cdot a^{\left(-3\right)\cdot \left(-1\right)}\cdot b^{1\cdot \left(-1\right)}=}$${\displaystyle 0,2a^3{b}^{-1}}$;

г) ${\displaystyle {\left(1\frac{1}{3}{a}^4{b}^{-2}\right)}^2=}$${\displaystyle {\left(\frac{4}{3}\right)}^2\cdot a^{4\cdot 2}\cdot b^{\left(-2\right)\cdot 2}=}$${\displaystyle \frac{16}{9}{a}^8{b}^{-4}}$;

ґ) ${\displaystyle {(-0,1ab)}^{-2}}$=

=${\displaystyle {\left(-0,1\right)}^{-2}\cdot a^{1\cdot \left(-2\right)}\cdot b^{1\cdot \left(-2\right)}=}$${\displaystyle 100a^{-2}{b}^{-2}}$;

д) ${\displaystyle {(-2m^5{n}^{-1})}^{-1}}$=

=${\displaystyle {\left(-2\right)}^{-1}\cdot m^{5\cdot \left(-1\right)}\cdot n^{\left(-1\right)\cdot \left(-1\right)}=}$${\displaystyle -0,5m^{-5}n}$.