Question

Вычислите:
1) (5/7)²*7/15;
2) (3/4)²*32/45;
3) (1/2)²*4/5;
4) (2 5/7)²*14/19;
5) (2 1/3)²*27/98;
6) (8/11)²*11/32;
7) (3/10)²*5/6;
8) (2/3)²*15/24;

Answer 1

воспользуемся математической аксиомой

$( frac{a}{b} )^n = frac{a^n}{b^n}$

тогда

1) $( frac{5}{7} )^2 * frac{7}{15} = frac{25}{49} * frac{7}{15} = frac{5}{7} * frac{1}{3} = frac{5}{21}$
2) $( frac{3}{4})^2 * frac{32}{45} = frac{9}{16} * frac{32}{45} = frac{1}{1} * frac{2}{5} = 0,4$
3) $( frac{1}{2})^2 * frac{4}{5} = frac{1}{4} * frac{4}{5} = frac{1}{5} = 0,2$
4) $(2 frac{5}{7} )^2 * frac{14}{19} = frac{361}{49} * frac{14}{19} = frac{19}{7} *2 = frac{38}{7} = 5 frac{3}{7}$
5) $(2 frac{1}{3})^2 * frac{27}{98} = frac{49}{9} * frac{27}{98} = frac{1}{1} * frac{3}{2} = 1,5$
6) $( frac{8}{11} )^2 * frac{11}{32} = frac{64}{121} * frac{11}{32} = frac{2}{11} * frac{1}{1} = frac{2}{11}$
7) $( frac{3}{10})^2 * frac{5}{6} = frac{9}{100} * frac{5}{6} = frac{3}{20} * frac{1}{2} = frac{3}{40}$
8) $( frac{2}{3})^2 * frac{15}{24} = frac{4}{9} * frac{15}{24} = frac{1}{3} * frac{5}{6} = frac{5}{18}$