Bài 1:

Ta có: 2009²⁰=(2009²)¹⁰=4036081¹⁰ ;  20092009¹⁰=20092009¹⁰

Vì 4036081¹⁰< 20092009¹⁰ => 2009²⁰< 20092009¹⁰

Bài 1:

Ta có:\(2009^{20}\)=\(2009^{10}\).\(2009^{10}\)

         \(20092009^{10}\)=(\(\left(2009.10001\right)^{10}=2009^{10}.10001^{10}\)

Vì 2009<10001\(\Rightarrow2009^{20}< 20092009^{10}\)

M=10²⁰⁰⁹+2/10²⁰⁰⁹-1=10²⁰⁰⁹-1+3/10²⁰⁰⁹-1=1+3/10^2009-1

N=10²⁰⁰⁹/10²⁰⁰⁹-3=10²⁰⁰⁹-3+3/10²⁰⁰⁹-3=1+3/10²⁰⁰⁹-3

vì 10²⁰⁰⁹-1>10²⁰⁰⁹-3

=>m<n

a)      Ta có: \(\frac{2}{{ - 5}} = \frac{{ - 16}}{{40}}\) và \(\frac{{ - 3}}{8} = \frac{{ - 15}}{{40}}\)

Do \(\frac{{ - 16}}{{40}} < \frac{{ - 15}}{{40}}\,\, \Rightarrow \,\frac{2}{{ - 5}} < \frac{{ - 3}}{8}\).

b)      Ta có: \( - 0,85 = \frac{{ - 85}}{{100}} = \frac{{ - 17}}{{20}}\). Vậy \( - 0,85\)=\(\frac{{ - 17}}{{20}}\).

c)      Ta có: \(\frac{{37}}{{ - 25}} = \frac{{ - 296}}{{200}}\)  

Do  \(\frac{{ - 137}}{{200}} > \frac{{ - 296}}{{200}}\) nên \(\frac{{ - 137}}{{200}}\) > \(\frac{{37}}{{ - 25}}\) .

d)      Ta có: \( - 1\frac{3}{{10}}=\frac{-13}{10}\) ;

\(-\left( {\frac{{ - 13}}{{ - 10}}} \right) = \frac{{-13}}{{10}}\).

Vậy \(- 1\frac{3}{{10}} =-(\frac{{-13}}{{-10}})\,\).

a: -3/4=-9/12

-5/6=-10/12

mà -9>-10

nên -3/4>-5/6

b: -5/17<0<2/7

c: 11/10>1>9/14

\(\frac{300}{670}\)>\(\frac{300}{677}\)mà \(\frac{300}{670}=\frac{30}{67}\)=>\(\frac{30}{67}\)>\(\frac{300}{677}\)(1)

Ta có :1-\(\frac{37}{67}\)=\(\frac{30}{67}\)và 1-\(\frac{377}{677}\)=\(\frac{300}{677}\)(2)

Từ (1) và (2) =>\(\frac{377}{677}\)>\(\frac{37}{67}\)

miki vs nha

Ta thấy :1-37/67=30/67 ; 1-377/677=300/677

Ta có : 30/67=300/670

Vì  300/670 >300/677 nên 37/67 < 377/677

Ta có :37/67=370/670

vì 370<670

=>370/670<1

370/670<(370+7)/(670+7)

cho nên 37/67<377/677