Mời thí chủ nhận bài:)), sai nhớ bảo tôi thí chủ đừng giấu:))
Ta có: 9³⁰= (3²)³⁰ = 3⁶⁰

27²⁰= (3³)²⁰ = 3⁶⁰

 9³⁰ = 27²⁰

so sánh 2²¹⁰ và 5¹⁴⁰

Ta có: 2²¹⁰= (2³)⁷⁰ = 8⁷⁰

5¹⁴⁰ = (5²)⁷⁰=25⁷⁰

Mà : 8⁷⁰ < 25⁷⁰

 2²¹⁰<5¹⁴⁰

\(9^{30}=\left(3^2\right)^{30}=3^{60}\)

\(27^{20}=\left(3^3\right)^{20}=3^{60}\)

\(3^{60}=3^{60}\)⇒\(9^{30}=27^{20}\)

Bài 3: 

Ta có: \(10^{20}=10^{2.10}=\left(10^2\right)^{10}=100^{10}\)

Vì \(90< 100\)\(\Rightarrow90^{10}< 100^{10}\)

hay \(10^{20}>90^{10}\)

Có: \(^{9^{36}}\)=\(^{\left(3^2\right)^{36}}\)=\(3^{72}\)

       \(27^{10}\)=\(\left(3^3\right)^{10}\)=\(3^{30}\)

Vì 3 mũ 72 > 3 mũ 30 suy ra 9 mũ 36 > 27 mũ 10

9^36=(3^3)^36=3^108

27^10=(3^9)^10=3^90

Suy ra 9^36>27^10

\(243^5=\left(3^5\right)^5=3^{25}\)

\(3.27^8=3.\left(3^3\right)^8=3.3^{24}=3^{25}\)

Vậy\(243^5=3.27^8\)

\(243^5=\left(3^5\right)^5=3^{25}\)

\(3.27^8=3.\left(3^3\right)^8=3.3^{24}=3^{25}\)

Vậy suy ra : \(243^5=3.27^8\)

Như đặc cầu

\(2^{333}< 3^{222}\)

a) Ta có :

\(27^{27}>27^{26}=\left(27^2\right)^{13}=729^{13}>243^{13}\)

\(\Rightarrow27^{27}>243^{13}\)

\(\Rightarrow-27^{27}< -243^{13}\)

\(\Rightarrow\left(-27\right)^{27}< \left(-243\right)^{13}\)

b) \(\left(\dfrac{1}{8}\right)^{25}>\left(\dfrac{1}{8}\right)^{26}=\left(\dfrac{1}{8^2}\right)^{13}=\left(\dfrac{1}{64}\right)^{13}>\left(\dfrac{1}{128}\right)^{13}\)

\(\Rightarrow\left(\dfrac{1}{8}\right)^{25}>\left(\dfrac{1}{128}\right)^{13}\)

\(\Rightarrow\left(-\dfrac{1}{8}\right)^{25}< \left(-\dfrac{1}{128}\right)^{13}\)

c) \(4^{50}=\left(4^5\right)^{10}=1024^{10}\)

\(8^{30}=\left(8^3\right)^{10}=512^{10}< 1024^{10}\)

\(\Rightarrow4^{50}>8^{30}\)

d) \(\left(\dfrac{1}{9}\right)^{17}< \left(\dfrac{1}{9}\right)^{12}< \left(\dfrac{1}{27}\right)^{12}\)

\(\Rightarrow\left(\dfrac{1}{9}\right)^{17}< \left(\dfrac{1}{27}\right)^{12}\)

a) Ta có :

2727>2726=(272)13=72913>243132727>2726=(272)13=72913>24313

⇒2727>24313⇒2727>24313

⇒−2727<−24313⇒−2727<−24313

⇒(−27)27<(−243)13⇒(−27)27<(−243)13

b) (18)25>(18)26=(182)13=(164)13>(1128)13(81​)25>(81​)26=(821​)13=(641​)13>(1281​)13

⇒(18)25>(1128)13⇒(81​)25>(1281​)13

⇒(−18)25<(−1128)13⇒(−81​)25<(−1281​)13

c) 450=(45)10=102410450=(45)10=102410

830=(83)10=51210<102410830=(83)10=51210<102410

⇒450>830⇒450>830

d) (19)17<(19)12<(127)12(91​)17<(91​)12<(271​)12

⇒(19)17<(127)12⇒(91​)17<(271​)12

Ta có : \(\frac{2^9}{3^{2010}}:\frac{3^9}{2^{2010}}=\frac{2^{2019}}{3^{2019}}=\left(\frac{2}{3}\right)^{2019}< 1^{2019}=1\)

Vì \(\frac{2^9}{3^{2010}}:\frac{3^9}{2^{2010}}< 1\)

=> \(\frac{2^9}{3^{2010}}< \frac{3^9}{2^{2010}}\)

       Bài làm :

Cách 1:

Ta có :

 \(\frac{2^9}{3^{2010}}\div\frac{3^9}{2^{2010}}=\frac{2^9.2^{2010}}{3^{2010}.3^9}=\frac{2^{2019}}{3^{2019}}=\left(\frac{2}{3}\right)^{2019}< 1\)

 \(\Rightarrow\frac{2^9}{3^{2010}}< \frac{3^9}{2^{2010}}\)

Cách 2 :

Nhận thấy :

\(\Rightarrow\frac{2^9}{3^{2010}}< \frac{3^9}{2^{2010}}\)