\(33^{44}>44^{33}>44^{32}\)

33 ⁴⁴ > 44 ³²

a: \(33^{44}>44^{33}>44^{32}\)

\(a,33^{44}=11^{44}\cdot3^{44}=11^{44}\cdot81^{11}>11^{33}\cdot64^{11}=11^{33}\cdot4^{33}=44^{33}>44^{32}\)

\(b,A=2000^{2016}\left(2000-1\right)+1999=1999\cdot2000^{2016}+1999⋮1999\)

`99^{20}=(99^{2})^{10}=(99.99)^{10}`

`9999^{10}=(99.101)^{10}`

Vì `(99.99)^{10}<(99.101)^{10}`

`->99^{20}<9999^{10}`

Ta có: \(99^{20}=\left(99^2\right)^{10}=9801^{10}\)

mà 9801<9999

nên \(99^{20}< 9999^{10}\)

5⁴⁸ và 11³²
=> 5^{32 + 16} và 11³²
=> 5³² x 5¹⁶ và 11³²
=> 5¹⁶ và 6³²
Biết 5 < 6 nên 5⁴⁸ < 11³²

2023²⁰²³ - 2023²⁰²² = 2023²⁰²².(2023 - 1) = 2023²⁰²².2022

2023²⁰²² - 2022²⁰²¹ = 2023²⁰²¹.(2023 - 1) = 2023²⁰²¹.2022

Do 2022 > 2021 ⇒ 2023²⁰²² > 2023²⁰²¹

⇒ 2023²⁰²².2022 > 2023²⁰²¹.2022

Vậy 2023²⁰²³ - 2023²⁰²² > 2023²⁰²² - 2023²⁰²¹

\(2^{30}< 2^{300}< 3^{200}\)

\(\Rightarrow2^{30}< 3^{200}\)

\(3^{200}=\left(3^2\right)^{100}=9^{100}=9^{30}\cdot9^{70}\)

Vì \(9>2\) nên \(9^{30}>2^{30}\) hay \(9^{30}\cdot9^{70}>2^{30}\)

Từ đó \(9^{100}>2^{30}\) hay \(2^{30}< 3^{200}\)

ta có :

2300=(23)100=8100

3200=(32)100=9100

vì 8100<9100 nên 2300<3200

Ví dụ như:  big(to) ,  small(nhỏ) ,  tall(cao) .

  happy(vui vẻ) ,  easy(dễ)  ...

khó

Nam is the tallest in my class.

HCM city is the most populated city in VN .

Madara is shorter than Mikey .

Your house is more expensive than my house .

His book is more beauty than my book .

Gaara is more handsome than Draken .

Fuji mount is more exciting than Ha Long bay .

Kimono is more expensive than Hanbok .

Comedy is funnier than action .

watch anime is the most exciting in the cinema .

lỗi!