№ 5.10 Алгебра = № 10.10 Математика
Спростіть вираз:
1. $ \frac{9m^2}{25a^2}\cdot\frac{35a^3}{18m^5};$
2. $\frac{7p^3}{18a^3}\cdot\left(-\frac{27a^4}{14p^3}\right);$
3. $ -\frac{5m^3}{21n^7}\cdot\frac{7n^2}{10m^4};$
4. $ -\frac{1}{18c^3d^4}\cdot\left(-\frac{12c^4d^4}{7}\right).$
Розв'язок:
1. $ \frac{9m^2}{25a^2}\cdot\frac{35a^3}{18m^5}=\frac{9m^2\cdot35a^3}{25a^2\cdot18m^5}=$
$= \frac{315a}{450m^3}=\frac{7a}{10m^3};$
2. $\frac{7p^3}{18a^3}\cdot\left(-\frac{27a^4}{14p^3}\right)=-\frac{7p^3\cdot27a^4}{18a^3\cdot14p^3}=$
$= -\frac{189a}{252}=-\frac{3a}{4};$
3. $ -\frac{5m^3}{21n^7}\cdot\frac{7n^2}{10m^4}=-\frac{5m^3\cdot7n^2}{21n^7\cdot10m^4}=$
$= -\frac{35}{210mn^5}=-\frac{1}{6mn^5};$
4. $ -\frac{1}{18c^3d^4}\cdot\left(-\frac{12c^4d^4}{7}\right)=$
$= \frac{12c^4d^4}{18c^3d^4\cdot7}=\frac{12c}{126}=\frac{2c}{21}.$