Question

Помогу решения пожалуста 4.11 4.12

Answer 1

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

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

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