227 Вправа 227Алгебра 8 клас Тарасенкова 2025 · § 6 · стор. 66

227. Спростіть вираз.

1) ${\displaystyle \frac{12x^{2}y}{a^4}\cdot \frac{a}{x{y}^2}\cdot \frac{a^{2}y}{6x^2}=}$${\displaystyle \frac{12a^3{x}^2{y}^2}{6a^4{x}^3{y}^2}=}$${\displaystyle \frac{\cancel{6a^3{x}^2{y}^2}\cdot 2}{\cancel{6a^3{x}^2{y}^2}\cdot ax}=}$${\displaystyle \frac{2}{ax}}$;

2) ${\displaystyle x^3{y}^2\cdot \frac{x^4}{15}\cdot \frac{5}{y^3}=}$${\displaystyle \frac{5x^7{y}^2}{15y^3}=}$${\displaystyle \frac{\cancel{5y^2}{x}^7}{\cancel{5y^2}\cdot 3y}=}$${\displaystyle \frac{x^7}{3y}}$;

3) ${\displaystyle \frac{a{b}^3}{x}\cdot \frac{a}{25b^2}\cdot \frac{35x}{a^3}=}$${\displaystyle \frac{35a^2{b}^{3}x}{25a^3{b}^{2}x}=}$${\displaystyle \frac{\cancel{5a^2{b}^{2}x}\cdot 7b}{\cancel{5a^2{b}^{2}x}\cdot 5a}=}$${\displaystyle \frac{7b}{5a}}$;

4) ${\displaystyle \frac{3}{2}\cdot \frac{m^2}{n^2}\cdot (-\frac{10m}{3n})\cdot \left(-\frac{1}{15mn}\right)=}$${\displaystyle \frac{30m^3}{90m{n}^4}=}$${\displaystyle \frac{\cancel{30m}{m}^2}{\cancel{30m}\cdot 3n^4}=}$${\displaystyle \frac{m^2}{3n^4}}$.