Question

помого пж дам 80 баллов номер 4.11

Answer 1

номер 4.11

1)дробь сокращается

$\frac{13 {}^{55} \times 13 {}^{40} }{13 {}^{94} } = \frac{13 {}^{95} }{13 {}^{94} } = 13$

4)

$\frac{19 {}^{77} \times 19 {}^{14} }{19 {}^{60} \times 19 {}^{29} } = \frac{19 {}^{91} }{19 {}^{89} } = 19 {}^{2}$

2)

$\frac{7 {}^{30} \times 7 {}^{27} }{7 {}^{56} } = \frac{7 {}^{57} }{7 {}^{56} } = 7$

5)

$\frac{3 {}^{75} \times 3 {}^{24} }{3 {}^{50} \times 3 {}^{48} } = \frac{3 {}^{99} }{3 {}^{98 } } = 3$

3)

$\frac{6 {}^{72} \times 6 {}^{20} }{6 {}^{72} \times 6 {}^{18} } = \frac{6 {}^{92} }{6 {}^{90} } = 6 {}^{2}$

6)

$\frac{2 {}^{120} \times 2 {}^{60} }{2 {}^{90} \times 2 {}^{44} } = \frac{2 {}^{180} }{2 {}^{134} } = 2 {}^{46}$

Answer 2

$1)\ \ \dfrac{(13^5)^{11}\cdot (13^4)^{10}}{(13^{47})^2}=\dfrac{13^{55}\cdot 13^{40}}{13^{94}}=\dfrac{13^{95}}{13^{94}}=13\\\\\\2)\ \ \dfrac{(7^5)^6\cdot 7^{27}}{(7^{14})^4}=\dfrac{7^{30}\cdot 7^{27}}{7^{56}}=\dfrac{7^{57}}{7^{56}}=7$

$3)\ \ \dfrac{(6^8)^9\cdot (6^4)^5}{(6^{24})^3\cdot (6^3)^6}=\dfrac{6^{72}\cdot 6^{20}}{6^{72}\cdot 6^{18}}=\dfrac{6^{92}}{6^{90}}=6^2=36\\\\\\4)\ \ \dfrac{(19^{11})^7\cdot (19^{7})^2}{(19^{20})^3\cdot 19^{29}}=\dfrac{19^{77}\cdot 19^{14}}{19^{60}\cdot 19^{29}}=\dfrac{19^{91}}{19^{89}}=19^{2}=361$

$5)\ \ \dfrac{(3^{15})^5\cdot (3^{12})^2}{(3^2)^{25}\cdot (3^3)^{16}}=\dfrac{3^{75}\cdot 3^{24}}{3^{50}\cdot 3^{48}}=\dfrac{3^{99}}{3^{98}}=3\\\\\\6)\ \ \dfrac{(2^{40})^3\cdot (2^{12})^5}{(2^{45})^2\cdot (2^{11})^4}=\dfrac{2^{120}\cdot 2^{60}}{2^{90}\cdot 2^{44}}=\dfrac{2^{180}}{2^{134}}=2^{46}$