\(5^{11}và7^7=\left(5.7\right)^4và\left(7.5\right)^2=35^4>35^2\)

5 mũ 11 > 7 mũ 7

\(\dfrac{5}{11}\) và \(\dfrac{7}{7}\)

Ta quy đồng:

\(\dfrac{35}{77}\) và \(\dfrac{77}{77}\)

\(\dfrac{35}{77}< \dfrac{77}{77}\)( Vì \(35< 77\) )

\(\Rightarrow\dfrac{5}{11}< \dfrac{7}{7}\)

222³³³ > 333²²² đó bạn

Câu này sáng nay mik làm rùi

222^333 = ( 222^3 )^111 = 10941048^111

333^222 = ( 333^2 )^111 = 110889^111

Vì 10941048^111 > 110889^111 nên 222^333 > 333^222

Ta có:

222³³³=(222³)¹¹¹=(2³.111³)¹¹¹=(8.111.111²)¹¹¹=(888.111²)¹¹¹

333²²²=(333²)¹¹¹=(3².111²)¹¹¹=(9.111²)^111.

Do 888>9=>222³³³>333^222.

Phân tích 2 phân số ta có:

1 = \(\dfrac{2017\times2019}{2017\times2019}\) = \(\dfrac{\left(2018-1\right)\times\left(2018+1\right)}{2017\times2019}\) = \(\dfrac{2018^2-1^2}{2017\times2019}\)

\(\dfrac{2018\times2018}{2017\times2019}\) = \(\dfrac{2018^2}{2017\times2019}\)

Vì \(2018^2\) > \(2018^2-1^2\) nên \(\dfrac{2018^2}{2017\times2019}\) > \(\dfrac{2018^2-1^2}{2017\times2019}\) hay \(\dfrac{2018\times2018}{2017\times2019}\) > 1

(Áp dụng hằng đẳng thức \(a^2-b^2\) = (a - b)(a + b))

\(2017\times2019=\left(2018-1\right)\times\left(2018+1\right)=2018\times2018+2018-2018-1=2018\times2018-1< 2018\times2018\)

\(\Rightarrow\dfrac{2018\times2018}{2017\times2019}>\dfrac{2018\times2018}{2018\times2018}=1\)

Cách 1:          \(\dfrac{3}{4}\) = 1 - \(\dfrac{1}{4}\); \(\dfrac{4}{5}\) = 1 - \(\dfrac{1}{5}\) Vì \(\dfrac{1}{4}\) > \(\dfrac{1}{5}\) nên \(\dfrac{3}{4}\) < \(\dfrac{4}{5}\)

Cách 2:    \(\dfrac{3}{4}\) = \(\dfrac{3\times4}{4\times4}\) = \(\dfrac{12}{16}\);  \(\dfrac{4}{5}\)  = \(\dfrac{4\times3}{5\times3}\)  = \(\dfrac{12}{15}\) vì \(\dfrac{12}{16}\)<\(\dfrac{12}{15}\)nên \(\dfrac{3}{4}\)< \(\dfrac{4}{5}\)

Cách 3:    \(\dfrac{3}{4}\) = \(\dfrac{3\times5}{4\times5}\) = \(\dfrac{15}{20}\);  \(\dfrac{4}{5}\)  =  \(\dfrac{4\times4}{5\times4}\) = \(\dfrac{16}{20}\) Vì \(\dfrac{15}{20}\)<\(\dfrac{16}{20}\) nên \(\dfrac{3}{4}\) < \(\dfrac{4}{5}\)

Ta co : 
2^150 =(2^3)^50 =8^50 
3^100 = (3^2)^50 = 9^50 
vi 8<9 hay 8^50 <9^50 vay 2^150 <3^100

Ta có:

\(2^{150}=2^{3.50}=\left(2^3\right)^{50}=8^{50}\)

\(3^{100}=3^{2.50}=\left(3^2\right)^{50}=9^{50}>8^{50}\)

\(\Rightarrow2^{150}< 3^{100}\)

2^150=(2^3)^50=8^50

3^100=(3^2)^50=9^50

Vì 9>8 nên 2^150<3^100

ko giải đâu

đùa thôi =)

bạn tra google là ra ngay ấy mà !!!

hông biết