Упр.5.31 ГДЗ Мордкович 8 класс (Алгебра)

1. 5.31. а) $$\frac{10y^5}{9a}:\frac{5y^3}{3b}\cdot\frac{3a^2}{by}$$; б) $$\frac{25a^3b^3}{14x^2y^4}\cdot\frac{21xy^3}{10a^2b^2}\cdot\frac{8xy^2}{15ab}$$; в) $$\frac{28a^2}{27x^3}:\frac{21x^4}{45y}\cdot\frac{x^8}{20ya}$$; г) $$\frac{45m^4}{49n^2t}\cdot\frac{56n^3}{27m^2}:\frac{20m^2n}{63t^2}$$.

а)

$$\frac{10y^5}{9a} : \frac{5y^3}{3b} \cdot \frac{3a^2}{by} = \frac{10y^5}{9a}\cdot \frac{3b}{5y^3}\cdot \frac{3a^2}{by}$$
$$= \frac{10\cdot 3\cdot 3 \cdot a^2 \cdot y^5 \cdot b}{9a\cdot 5y^3 \cdot by} = \frac{2ay}{1} =2ay$$

б)

$$\frac{25a^3b^3}{14x^2y^4}\cdot \frac{21xy^3}{10a^2b^2}\cdot \frac{8xy^2}{15ab}$$
$$= \frac{25\cdot 21\cdot 8 \cdot a^3b^3 \cdot x \cdot x \cdot y^3 \cdot y^2}{14\cdot 10\cdot 15 \cdot x^2y^4 \cdot a^2b^2 \cdot ab} = \frac{2y}{1} =2y$$

в)

$$\frac{28a^2}{27x^3} : \frac{21x^4}{45y}\cdot \frac{x^8}{20ya} = \frac{28a^2}{27x^3}\cdot \frac{45y}{21x^4}\cdot \frac{x^8}{20ya}$$
$$= \frac{28\cdot 45}{27\cdot 21\cdot 20}\cdot \frac{a^2x^8}{x^3x^4ay} = \frac{4a\cdot 5\cdot x}{3\cdot 3\cdot 20} = \frac{ax}{9}$$

г)

$$\frac{45m^4}{49n^2t}\cdot \frac{56n^3}{27m^2} : \frac{20m^2n}{63t^2} = \frac{45m^4}{49n^2t}\cdot \frac{56n^3}{27m^2}\cdot \frac{63t^2}{20m^2n}$$
$$= \frac{45\cdot 56\cdot 63}{49\cdot 27\cdot 20}\cdot \frac{m^4n^3t^2}{m^2m^2n^2n t} = \frac{5\cdot 8\cdot 63}{7\cdot 3\cdot 20}\cdot 3t =6t$$

Ответ

а) $$2ay$$; б) $$2y$$; в) $$\frac{ax}{9}$$; г) $$6t$$.