№ 6.13 Алгебра = № 11.13 Математика
Виконайте дії:
1. $\frac{4a^2}{5b^3}:\frac{8a^3}{7c^3}:\frac{14c^2}{15b^2};$
2. $\frac{2a^3}{25b^3}\cdot\frac{10b^2}{3c^4}:\frac{4a^2}{15bc};$
3. $\frac{c^3}{18p^4}:\left(\frac{9c^2}{20p^3}:\frac{27c^3p}{10}\right);$
4. $\frac{115a^3}{34b^4}:\frac{92a^6}{51b^3}\cdot\frac{4b^2}{15a^2}.$
Розв'язок:
1. $\frac{4a^2}{5b^3}:\frac{8a^3}{7c^3}:\frac{14c^2}{15b^2}=\frac{4a^2\cdot7c^3\cdot15b^2}{5b^3\cdot8a^3\cdot14c^2}=$
$= \frac{3c}{4ab};$
2. $\frac{2a^3}{25b^3}\cdot\frac{10b^2}{3c^4}:\frac{4a^2}{15bc}=$
$= \frac{2a^3\cdot10b^2\cdot15bc}{25b^3\cdot3c^4\cdot4a^2}=$
$= \frac{a^3b^3c}{a^2b^3c^4}=\frac{a}{c^3};$
3. $\frac{c^3}{18p^4}:\left(\frac{9c^2}{20p^3}:\frac{27c^3p}{10}\right)=$
$= \frac{c^3}{18p^4}:\frac{9c^2\cdot10}{20p^3\cdot27c^3p}=$
$= \frac{c^3\cdot6p^4c}{18p^4\cdot1}=\frac{c^4}{3};$
4. $\frac{115a^3}{34b^4}:\frac{92a^6}{51b^3}\cdot\frac{4b^2}{15a^2}=$
$= \frac{115a^3\cdot51b^3\cdot4b^2}{34b^4\cdot92a^6\cdot15a^2}=$
$= \frac{a^3b^5}{2a^8b^4}=\frac{b}{2a^5}.$