Question

Помогу решения пожалуста 4.11 4.12

Answer 1

$4.11.; ; frac{(13^5)^{11}cdot (13^4)^{10}}{(13^{47})^2}=frac{13^{55}cdot 13^{40}}{13^{94}}=13^{55+40-94}=13^{1}=13\\frac{(7^5)^6cdot 7^{27}}{(7^{14})^4}=frac{7^{30}cdot 7^{27}}{7^{56}}=7^{30+27-56}=7^{1}=7\\frac{(6^8)^9cdot (6^4)^5}{(6^{24})^3cdot (6^3)^6}=frac{6^{72}cdot 6^{20}}{6^{72}cdot 6^{18}}=frac{6^{92}}{6^{90}}=6^2=36\\frac{(19^{11})^7cdot (19^{7})^2}{(19^{20})^3cdot 19^{29}}=frac{19^{77}cdot 19^{14}}{19^{60}cdot 19^{29}}=frac{19^{91}}{19^{89}}=19^2=361$

$frac{(3^{15})^5cdot (3^{12})^2}{(3^2)^{25}cdot (3^3)^{16}}=frac{3^{75}cdot 3^{24}}{3^{50}cdot 3^{48}}=frac{3^{99}}{3^{98}}=3\\frac{(2^{40})^3cdot (2^{12})^5}{(2^{45})^2cdot (2^{11})^4}=frac{2^{120}cdot 2^{60}}{2^{90}cdot 2^{44}}=frac{2^{180}}{2^{134}}=2^{46}$

$4.12.; ; (y^4)^5:(y^9)^2cdot y^3=frac{y^{20}cdot y^3}{y^{18}}=y^{23-18}=y^5=(-1)^5=-1\\(z^3)^9:(z^4)^6cdot z=frac{z^{27}cdot z}{z^{24}}=z^{28-24}=z^4=(-2)^4=2^4=16$