№ 5.17 Алгебра = № 10.17 Математика
Спростіть вираз:
1. $\frac{54a^2c}{81b^3}\cdot\frac{32ab}{13c^3}\cdot\frac{52bc^2}{128a^3};$
2. $\frac{147x^4y^2}{p^3}\cdot10xp^2\cdot\frac{y^3}{105x^5y}.$
Розв'язок:
1. $\frac{54a^2c}{81b^3}\cdot\frac{32ab}{13c^3}\cdot\frac{52bc^2}{128a^3}=$
$=\frac{54a^2c\cdot32ab\cdot52bc^2}{81b^3\cdot13c^3\cdot128a^3}=$
$= \frac{2a^3b^2c^3}{3a^3b^3c^3}=\frac{2}{3b};$
2. $\frac{147x^4y^2}{p^3}\cdot10xp^2\cdot\frac{y^3}{105x^5y}=$
$= \frac{147x^4y^2\cdot10xp^2\cdot y^3}{p^3\cdot105x^5y}=$
$= \frac{14x^5y^5p^2}{x^5yp^3}=\frac{14y^4}{p}.$