885 Вправа 885Алгебра 8 клас Бевз 2025 · § 17 · стор. 165

885. Спрости вираз.

а) ${\displaystyle 0,2x^{-2}y\cdot 5x^2{y}^{-2}=}$${\displaystyle \left(0,2\cdot 5\right)\cdot x^{-2+2}\cdot y^{1-2}}$=

=${\displaystyle 1\cdot x^0\cdot y^{-1}=}$${\displaystyle \frac{1}{y}}$;

б) ${\displaystyle (a^{-1}+b^{-1})\cdot {(a+b)}^{-1}=}$${\displaystyle (\frac{1}{a}+\frac{1}{b})\cdot \frac{1}{a+b}}$=

=${\displaystyle \frac{\cancel{b+a}}{ab}\cdot \frac{1}{\cancel{a+b}}=}$${\displaystyle \frac{1}{ab}}$;

в) ${\displaystyle {\left(\frac{m^4{n}^{-2}}{9p}\right)}^2{\left(\frac{m^2{n}^{-3}}{3p}\right)}^{-3}=}$${\displaystyle \frac{m^8{n}^{-4}}{81p^2}\cdot \frac{27p^3}{m^6{n}^{-9}}}$=

=${\displaystyle \frac{27m^8{n}^{-4}{p}^3}{81m^6{n}^{-9}{p}^2}=}$${\displaystyle \frac{m^2{n}^{5}p}{3}}$;

г) ${\displaystyle {\left(\frac{a^4{b}^{-3}}{c^5}\right)}^{-3}{\left(\frac{c^8}{a{b}^3}\right)}^2=}$${\displaystyle \frac{a^{-12}{b}^9}{c^{-15}}\cdot \frac{c^{16}}{a^2{b}^6}}$=

=${\displaystyle a^{-12-2}{b}^{9-6}{c}^{16+15}=}$${\displaystyle \frac{b^3{c}^{31}}{a^{14}}}$.