458 Вправа 458Алгебра 8 клас Бевз 2025 · § 9 · стор. 92

458. Спрости вираз.

а) ${\displaystyle 0,5x^{-6}{y}^2\cdot 4x^7{y}^{-2}}$=

=${\displaystyle \left(0,5\cdot 4\right)\cdot x^{-6+7}\cdot y^{2-2}=}$${\displaystyle 2x}$;

б) ${\displaystyle 8a^{-3}{b}^3\cdot 0,25a^5{b}^{-1}}$=

=${\displaystyle \left(8\cdot 0,25\right)\cdot a^{-3+5}\cdot b^{3-1}=}$${\displaystyle 2a^2{b}^2}$;

в) ${\displaystyle 9a^6{b}^{-2}:(-3a^2{b}^{-5})}$=

=${\displaystyle -\frac{9}{3}\cdot a^{6-2}\cdot b^{-2+5}=}$${\displaystyle -3a^4{b}^3}$;

г) ${\displaystyle \frac{12x^2}{7y^7}\cdot \frac{14y^9}{3x^{-2}}=}$${\displaystyle \frac{12\cdot 14}{7\cdot 3}\cdot x^{2+2}\cdot y^{-7+9}=}$${\displaystyle 8x^4{y}^2}$;

ґ) ${\displaystyle \frac{16a^4{b}^6}{c^7}:\frac{8b^6{c}^{-6}}{3a^{-3}}=}$${\displaystyle \frac{16\cdot 3}{8}\cdot a^{4-3}\cdot b^{6-6}\cdot c^{-7+6}}$=

=${\displaystyle 6a{c}^{-1}=}$${\displaystyle \frac{6a}{c}}$;

д) ${\displaystyle \left(\frac{a^{-3}{b}^4}{5}\right):{\left(\frac{10}{a^{-2}{b}^3}\right)}^{-3}=}$${\displaystyle \frac{a^{-3}{b}^4}{5}:\frac{{\left(a^{-2}{b}^3\right)}^3}{10^3}}$=

=${\displaystyle \frac{a^{-3}{b}^4}{5}:\frac{a^{-6}{b}^9}{1000}=}$${\displaystyle \frac{1000}{5}\cdot a^{-3+6}\cdot b^{4-9}}$=

=${\displaystyle 200a^3{b}^{-5}=}$${\displaystyle \frac{200a^3}{b^5}}$;

е) ${\displaystyle 4a^7{c}^{-1}\cdot {\left(\frac{ac}{5}\right)}^{-1}=}$${\displaystyle 4a^7{c}^{-1}\cdot \frac{5}{ac}}$=

=${\displaystyle \left(4\cdot 5\right)\cdot a^{7-1}\cdot c^{-1-1}=}$${\displaystyle 20a^6{c}^{-2}=}$${\displaystyle \frac{20a^6}{c^2}}$;

є) ${\displaystyle \frac{a^{-2}}{9c^3}:{\left(\frac{3a^2}{c^{-2}}\right)}^{-3}=}$${\displaystyle \frac{a^{-2}}{9c^3}\cdot {\left(\frac{3a^2}{c^{-2}}\right)}^3=}$${\displaystyle \frac{a^{-2}}{9c^3}\cdot {\left(3a^2{c}^2\right)}^3}$=

=${\displaystyle \frac{a^{-2}}{9c^3}\cdot 27a^6{c}^6=}$${\displaystyle \frac{27}{9}\cdot a^{-2+6}\cdot c^{-3+6}=}$${\displaystyle 3a^4{c}^3}$.