a) \(16^{12}=4^{2\cdot12}=4^{24}\)

\(64^8=4^{4\cdot8}=4^{32}\)

=>\(64^8>16^{12}\)

b) 

\(5^{23}=5.5^{22}\)

=> \(6.5^{22}>5^{23}\)

a/ Ta có :

\(5^{36}=\left(5^3\right)^{12}=125^{12}\)

\(11^{24}=\left(11^2\right)^{12}=121^{12}\)

Vì \(125^{12}>121^{12}\Leftrightarrow5^{36}>11^{24}\)

b/ Ta có :

\(5^{23}< 6.5^{22}\)

a, \(5^{36}\) và \(11^{24}\)

Ta có:

\(5^{36}\) = \(\left(5^3\right)^{12}\)= \(125^{12}\)

Và \(11^{24}\) = \(\left(11^2\right)^{12}\)= \(121^{12}\)

vì \(125^{12}\)> \(121^{12}\)

Nên \(5^{36}\) > \(11^{24}\)

b, \(5^{23}\) và 6. \(5^{22}\)

Mà \(5^{23}\)= 5. \(5^{22}\)

=> 5. \(5^{22}\) < 6. \(5^{22}\)

Nên \(5^{23}\) < 6. \(5^{22}\)

4^5<64²

36²>6⁵

125⁴>25³

GIẢi THÍCH RÕ RA HỘ MK

a) 27¹¹ = ( 3² ) ¹¹ = 3^2.11 = 3²²

   81⁸ = ( 3⁴ ) ⁸ = 3^4.8 = 3³²

Vì 22 < 32 nên 3²² < 3³² hay 27¹¹ < 81⁸

b) 625⁵ = ( 5⁴ ) ⁵ = 5^4.5 = 5²⁰

   125⁷ = ( 5³ ) ⁷ = 5^3.7 = 5²¹

Vì 20 < 21 nên 5²⁰ < 5²¹ hay 625⁵ < 125⁷

c) 5²³ = 5²² . 5

    6 . 5²² giữ nguyên

Vì 5 < 6 nên 5²³ < 6 . 5²²

d) 7 . 2¹³ giữ nguyên

   2¹⁶ = 2¹³ . 2³ = 2¹³ . 8

Vì 7 < 8 nên 7 . 2¹³ < 2¹⁶

27¹¹ và 81⁸

(3³)¹¹ = 3³³ , (3⁴)⁸ = 3³² => 27¹¹ >81⁸

\(5^{36}\)và  \(11^{24}\)

Ta có : 

\(5^{36}=\left(5^3\right)^{12}=125^{12}\)

\(11^{24}=\left(11^2\right)^{12}=121^{12}\)

Vi \(125>121\)nên \(5^{36}>11^{24}\)

\(3^{100}\)và   \(2^{150}\)

Ta có : 

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

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

Vì \(9>8\)nên \(3^{100}>2^{150}\)

a)\(27^{11}=3^{33}>3^{32}=81^8\)

b)\(2^{5000}=32^{1000}>25^{1000}=5^{2000}\)

c)\(5^{36}=125^{12}>121^{12}=11^{24}\)

d)\(3^2>2^3\Rightarrow3^{2n}>2^{3n}\)\(n\in\)N*

a) Ta có:

\(27^{11}=\left(3^3\right)^{11}=3^{33}\)

\(81^8=\left(3^4\right)^8=3^{32}\)

Vì 33>32 \(\Rightarrow\)3³³ > 3³² hay 27¹¹ > 81⁸

b) Ta có :

2⁵⁰⁰⁰ = \(\left(2^5\right)^{1000}=32^{1000}\)

\(5^{2000}=\left(5^2\right)^{1000}=25^{1000}\)

Vì 32 > 25 \(\Rightarrow\)32^1000 > 25^1000 hay 2^5000 > 5^2000

c) Ta có:

5^36 = 5^12.3 = (5^3)^12 = 125^12

11^24 = 11^12.2 = (11^2)^13 = 121^12

Vì 125>121 => 125^12>121^12 hay 5^36>11^24

5³⁶ = (5³)¹² = 125¹²

11²⁴ = (11²)¹² = 121¹²

mà 125 > 121 nên 125¹² > 121¹²

Vậy 5³⁶ > 11²⁴

5 ^ 36 = 5 ^ 3 x 12 =  ( 5 ^ 3 ) ^ 12 = 125 ^ 12

11 ^ 24 = 11 ^ 2 x 12 = ( 11 ^ 2 ) ^ 12 = 121 ^ 12

Vi 121 < 125 nen 121 ^ 12 < 125 ^ 12 hay 5 ^ 36 > 11 ^ 24

Tích cho mik nha

a) ta cs: 36⁴⁵ - 36⁴⁴ = 36⁴⁴.(36-1) =36⁴⁴.35

36⁴⁴ - 36⁴³ = 36⁴³.35

=> 36⁴⁵ - 36⁴⁴ > 36⁴⁴ - 36⁴³

b) ta cs: 3⁴⁵⁰ = (3³)¹⁵⁰ = 27¹⁵⁰

5³⁰⁰ = (5²)¹⁵⁰ = 25¹⁵⁰

=> 3⁴⁵⁰ > 5³⁰⁰

c) ta cs: 345² = 345.345 = 345.(342+ 3) = 345.342 + 345.3

342 . 348 = 342.(345+3) = 342.345 + 342.3

=> 345² > 342.348

d) ta cs: (1+2+3+4)² = 10² =100

1³ + 2³ + 3³ + 4³ = 100

=>...

Ta có :

5³⁶ = ( 5³ )¹² = 125¹²

11²⁴ = ( 11² )¹² = 121¹²

vì 125¹² > 121¹² nên 5³⁶ > 11²⁴

5^36 > 11^24

k mik nha !

mik giải rồi thanks nha !