Question

Сделайте 4.11 от одного до шести и 4.13.Даю примерно 16 баллов

Answer 1

HJtiение:

4.11.

$1) \frac{(13^5)^{11}*(13^4)^{10}}{(13^{47})^2} = \frac{13^{55}*13^{40}}{13^{94}} = \frac{13^{95}}{13^{94}} = 13^1 = 13$

$2) \frac{(7^5)^6*7^{27}}{(7^{14})^4} = \frac{7^{30}*7^{27}}{7^{56}} = \frac{7^{57}}{7^{56}} = 7^1 = 7$

$3) \frac{(6^8)^9*(6^4)^5}{(6^{24})^3*(6^3)^6} = \frac{6^{72}*6^{20}}{6^{72}*6^{18}} = 6^2 = 36$

$4) \frac{(19^{11})^7*(19^7)^2}{(19^{20})^3*19^{29}} = \frac{19^{77}*19^{14}}{19^{60}*19^{29}} = \frac{19^{91}}{19^{89}} = 19^2 = 361$

$5) \frac{(3^{15})^5*(3^{12})^2}{(3^2)^{25}*(3^3)^{16}} = \frac{3^{75}*3^{24}}{3^{50}*3^{48}} = \frac{3^{98}}{3^{98}} = 1$

$6) \frac{(2^{40})^3*(2^{12})^5}{(2^{45})^2*(2^{11})^4} = \frac{2^{120} * 2^{60}}{2^{90}*2^{44}} = \frac{2^{180}}{2^{134}} = 2^{46}$

4.13.

$1) (a^{2k})^5 : (2a^{3k}) - 1,5a^{79} = -a^{7k}\\\\\frac{a^{10k}}{2a^{3k}} - 1,5a^{79} = -a^{7k}\\\\0,5a^{10k-3k} - 1,5a^{7k} = -a^{7k}\\\\0,5a^{7k} - 1,5a^{7k} = -a^{7k}\\\\-a^{7k} = -a^{7k}$

$2) (y^{2n})^6 : (5y^{5n})^2 + 0,96y^{2n} = y^{2n}\\\\\frac{y^{12n}}{25y^{10n}} + 0,96y^{2n} = y^{2n}\\\\0,04y^{2n} + 0,96y^{2n} = y^{2n}\\\\y^{2n} = y^{2n}$