`a, -21/15 . (-10)/14 = 210/210=1`

`b, (-2/3)^2= 4/9`

`c, (-3)/4 . (-4)/5 . 16/9= 192/180=16/15`

`d, (-8)/3 . 5/6= -40/18=-20/9`

`e, 16/30 . 5/12= 8/15 . 5/12=40/180=2/9`

`f, 13/30 . (-1)/5= -13/150`

`g, 2/21 . 3/28= 6/588= 1/98`

`h, (-3/4)^3= -27/64`

a, Ta có : \(10^{15}\cdot11=10^{15}\left(10+1\right)=10^{16}+10^{15}\)

Vì \(10^{16}+10^{15}>10^{16}+10\)

\(\Rightarrow\dfrac{10^{16}+10^{15}}{10^{16}+1}>\dfrac{10^{16}+10}{10^{16}+1}\)

Hay A>B

b, Ta có : \(C=\dfrac{10^{10}+1}{10^{10}-1}=\dfrac{10^{10}}{10^{10}-1}+\dfrac{1}{10^{10}-1}\)

\(D=\dfrac{10^{10}-1}{10^{13}-3}=\dfrac{10^{10}}{10^{13}-3}+\dfrac{-1}{10^{13}-3}\)

Vì \(\dfrac{10^{10}}{10^{10}-1}>\dfrac{10^{10}}{10^{13}-3};\dfrac{1}{10^{10}-1}>\dfrac{-1}{10^{13}-3}\)

\(\Rightarrow\dfrac{10^{10}+1}{10^{10}-1}>\dfrac{10^{10}-1}{10^{13}-3}\)

Hay C > D

a) \(\dfrac{2}{5}-\dfrac{3}{15}\)

\(=\dfrac{2}{5}-\dfrac{3:3}{15:3}\)

\(=\dfrac{2}{5}-\dfrac{1}{5}\)

\(=\dfrac{1}{5}\)

b) \(\dfrac{9}{27}-\dfrac{2}{9}\)

\(=\dfrac{9:3}{27:3}-\dfrac{2}{9}\)

\(=\dfrac{3}{9}-\dfrac{2}{9}\)

\(=\dfrac{1}{9}\)

c) \(\dfrac{18}{24}-\dfrac{4}{8}\)

\(=\dfrac{18:6}{24:6}-\dfrac{4:2}{8:2}\)

\(=\dfrac{3}{4}-\dfrac{2}{4}\)

\(=\dfrac{1}{4}\)

d) \(\dfrac{6}{16}-\dfrac{10}{64}\)

\(=\dfrac{6\times2}{16\times2}-\dfrac{10:2}{64:2}\)

\(=\dfrac{12}{32}-\dfrac{5}{32}\)

\(=\dfrac{7}{32}\)

2/

a/ \(\dfrac{7}{10}=\dfrac{7.15}{10.15}=\dfrac{105}{150}\)

\(\dfrac{11}{15}=\dfrac{11.10}{15.10}=\dfrac{110}{150}\)

-Vì \(\dfrac{105}{150}< \dfrac{110}{150}\)(105<110)nên \(\dfrac{7}{10}< \dfrac{11}{15}\)

b/ \(\dfrac{-1}{8}=\dfrac{-1.3}{8.3}=\dfrac{-3}{24}\)

-Vì \(\dfrac{-3}{24}>\dfrac{-5}{24}\left(-3>-5\right)\)nên\(\dfrac{-1}{8}>\dfrac{-5}{24}\)

c/\(\dfrac{25}{100}=\dfrac{25:25}{100:25}=\dfrac{1}{4}\)

\(\dfrac{10}{40}=\dfrac{10:10}{40:10}=\dfrac{1}{4}\)

-Vì \(\dfrac{1}{4}=\dfrac{1}{4}\)nên\(\dfrac{25}{100}=\dfrac{10}{40}\)

a/ \(\dfrac{7}{10}< \dfrac{11}{15}\)

c/ \(\dfrac{25}{100}=\dfrac{10}{40}\)

a) 

b) 

c) \(\dfrac{25}{100}=\dfrac{10}{40}\)

a: \(A=\dfrac{2^{12}\cdot3^{10}+2^3\cdot2^9\cdot3^9\cdot3\cdot5}{2^{12}\cdot3^{12}+2^{11}\cdot3^{11}}\)

\(=\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{11}\cdot3^{11}\cdot7}\)

\(=\dfrac{2^{12}\cdot3^{10}\cdot6}{2^{11}\cdot3^{11}\cdot7}=\dfrac{2}{3}\cdot\dfrac{6}{7}=\dfrac{12}{21}=\dfrac{4}{7}\)

b: \(B=\left(\dfrac{12}{105}+\dfrac{9^{15}}{3}\right)\cdot\dfrac{1}{3}\cdot\dfrac{6^8}{6^4\cdot2^4}\)

\(=\dfrac{12+35\cdot9^{15}}{105}\cdot\dfrac{1}{3}\cdot3^4\)

\(=\dfrac{12+35\cdot9^{15}}{105}\cdot3^3=\dfrac{9\left(12+35\cdot9^{15}\right)}{35}\)

\(a,\left(\dfrac{7}{20}+\dfrac{11}{15}-\dfrac{15}{12}\right):\left(\dfrac{11}{20}-\dfrac{26}{45}\right).\)

\(=\left(\dfrac{21}{60}+\dfrac{44}{60}-\dfrac{75}{60}\right):\left(\dfrac{99}{180}-\dfrac{104}{180}\right).\)

\(=\left(\dfrac{65}{60}-\dfrac{75}{60}\right):\left(-\dfrac{5}{180}\right).\)

\(=-\dfrac{10}{60}:\left(-\dfrac{5}{180}\right).\)

\(=-\dfrac{1}{6}:\left(-\dfrac{1}{36}\right).\)

\(=-\dfrac{1}{6}.\left(-36\right).\)

\(=\dfrac{-1.\left(-36\right)}{6}=\dfrac{36}{6}=6.\)

Vậy......

\(b,\dfrac{5-\dfrac{5}{3}+\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}+\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{16}{121}}.\)

\(=\dfrac{5\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}{8\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}:\dfrac{15\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}{16\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}.\)

\(=\dfrac{5}{8}:\dfrac{15}{16}.\)

\(=\dfrac{5}{8}.\dfrac{16}{15}=\dfrac{5.16}{8.15}=\dfrac{1.2}{1.3}=\dfrac{2}{3}.\)

Vậy......

c, (làm tương tự câu b).

~ Học tốt!!! ~

Có:\(10A=\dfrac{10^{16}+10}{10^{16}+1}=\dfrac{10^{16}+1+9}{10^{16}+1}=\dfrac{10^{16}+1}{10^{16}+1}+\dfrac{9}{10^{16}+1}=1+\dfrac{9}{10^{16}+1}\)

\(10B=\dfrac{10^{17}+10}{10^{17}+1}=\dfrac{10^{17}+1+9}{10^{17}+1}=\dfrac{10^{17}+1}{10^{17}+1}+\dfrac{9}{10^{17}+1}=1+\dfrac{9}{10^{17}+1}\)

\(1+\dfrac{9}{10^{16}+1}>1+\dfrac{9}{10^{17}+1}\Rightarrow A>B\)

Vậy \(A>B\)

a) \(\dfrac{6}{14}=\dfrac{6:2}{14:2}=\dfrac{3}{7}\)

\(\dfrac{3}{7}< \dfrac{4}{7}\)

b) \(\dfrac{6}{15}=\dfrac{6:3}{15:3}=\dfrac{2}{5}\)

\(\dfrac{3}{5}>\dfrac{2}{5}\)

c) \(\dfrac{10}{18}=\dfrac{10:2}{18:2}=\dfrac{5}{9}\)

\(\dfrac{5}{9}>\dfrac{2}{9}\)