№ 413 Алгебра = № 15.16 Математика
Умова:
Спростіть вираз:
$1) \ 15m^2 \cdot (4m^3)^2; \\$
$2) \ -0{,}5m^5 \cdot (2m^3)^4; \\$
$3) \ (-3a^3b^4)^4 \cdot \left( -\frac{1}{81} ab^3 \right); \\$
$4) \ \left( -\frac{2}{3} a c^4 \right)^3 \cdot 18a^5 c.$
Розв'язок:
1) 15m2 ∙ (4m3)2 = 15m2 ∙ 16m6 = 240m8;
2) –0,5m5 ∙ (2m3)4 = –0,5m5 ∙ 16m12 = –8m17;
3) (–3a3b4)4 ∙ (–$\frac{1}{81}$ab3) = 81a12b16 ∙ (–$\frac{1}{81}$ab3) = –a13b19;
4) (–$\frac{2}{3}$ac4)3 ∙ 18a5c = –$\frac{8}{27}$ ∙ $\frac{18}{1}$a3c12a5c = –$\frac{16}{3}$a8c13 = –5$\frac{1}{3}$a8c13.