`#3107.101107`

a)

`64^150` và `4^450`

Ta có:

`64^150 = (4^3)^150 = 4^(3*150) = 4^450`

Vì `450 = 450 => 4^450 = 4^450 => 64^150 = 4^450`

Vậy, `64^150 = 4^450`

b)

`81^64` và `27^100`

Ta có:

`81^64 = (3^4)^64 = 3^(4*64) = 3^256`

`27^100 = (3^3)^100 = 3^(3*100) = 3^300`

Vì `256 < 300 => 3^256 < 3^300 => 81^64 < 27^100`

Vậy, `81^64 < 27^100`

c)

`125^1000` và `25^3000`

Ta có:

`125^1000 = (5^3)^1000 = 5^(3*1000) = 5^3000`

Vì `5 < 25 => 5^3000 < 25^3000 => 125^1000 < 25^3000`

Vậy, `125^1000 < 25^3000`

d)

`4^30` và `3^40`

Ta có:

`4^30 = 4^(3*10) = (4^3)^10 = 64^10`

`3^40 = 3^(4*10) = (3^4)^10 = 81^10`

Vì `64 < 81 => 64^10 < 81^10 => 4^30 < 3^40`

Vậy, `4^30 < 3^40`

m)

`2^5000` và `5^2000`

Ta có:

`2^5000 = 2^(5*1000) = (2^5)^1000 = 32^1000`

`5^2000 = 5^(2*1000) = (5^2)^1000 = 25^1000`

Vì `32 > 25 => 32^1000 > 25^1000 => 2^5000 > 5^2000`

Vậy, `2^5000 > 5^2000`

h)

`6^450` và `3^750`

Ta có:

`6^450 = 6^(150*3) = (6^3)^150 = 216^150`

`3^750 = 3^(150*5) = (3^5)^150 = 243^150`

Vì `216 < 243 => 216^150 < 243^150 => 6^450 < 3^750`

Vậy, `6^450 < 3^750`

0)

`333^444` và `444^333`

Ta có:

`333^444 = 333^(4*111) = (333^4)^111 = (3^4 *111^4)^111 = 81^111 * 111^444`

`444^333 = 444^(3*111) = (444^3)^111 = (4^3 * 111^3)^111 = 64^111 * 111^333`

Vì `81 > 64;` `111^444 > 111^333`

`=> 81^111 * 111^444 > 64^111 * 111^333`

Vậy, `333^444 > 444^333.`

a) Ta có:

\(64^{150}=\left(2^6\right)^{150}=2^{900}\)

\(4^{450}=\left(2^2\right)^{450}=2^{900}\)

Mà: \(2^{900}=2^{900}\Rightarrow64^{150}=4^{450}\)

b) Ta có:

\(81^{64}=\left(3^4\right)^{64}=3^{256}\)

\(27^{100}=\left(3^3\right)^{100}=3^{300}\)

Mà: \(3^{300}>3^{256}\Rightarrow27^{100}>81^{64}\)

c) Ta có: 

\(125^{1000}=\left(5^3\right)^{1000}=5^{3000}\)

Mà: \(25^{3000}>5^{3000}\Rightarrow25^{3000}>125^{1000}\)

d) Ta có:

\(4^{30}=\left(4^3\right)^{10}=64^{10}\)

\(3^{40}=\left(3^4\right)^{10}=81^{10}\)

Mà: \(81^{10}>64^{10}\Rightarrow3^{40}>4^{30}\)

m) Ta có:

\(2^{5000}=\left(2^5\right)^{1000}=32^{1000}\)

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

Mà: \(25^{1000}< 32^{1000}\Rightarrow2^{5000}>5^{2000}\)

h) Ta có:

\(6^{450}=\left(6^3\right)^{150}=216^{150}\)

\(3^{750}=\left(3^5\right)^{150}=243^{150}\)

Mà: \(243^{150}>216^{150}\Rightarrow3^{750}>6^{450}\)

.... 

a) 4⁴⁵⁰ = (4³)¹⁵⁰ = 64¹⁵⁰

b) 81⁶⁴ = (3⁴)⁶⁴ = 3²⁵⁶

27¹⁰⁰ = (3³)¹⁰⁰ = 3³⁰⁰

Do 256 < 300 nên 3²⁵⁶ < 3³⁰⁰

Vậy 81⁶⁴ < 27¹⁰⁰

c) 125¹⁰⁰⁰ = (5³)¹⁰⁰⁰ = 5³⁰⁰⁰

Do 5 < 25 nên 5³⁰⁰⁰ < 25³⁰⁰⁰

Vậy 125¹⁰⁰⁰ < 25³⁰⁰⁰

d) 4³⁰ = (4³)¹⁰ = 64¹⁰

3⁴⁰ = (3⁴)¹⁰ = 81¹⁰

Do 64 < 81 nên 64¹⁰ < 81¹⁰

Vậy 4³⁰ < 3⁴⁰

m) 2⁵⁰⁰⁰ = (2⁵)¹⁰⁰⁰ = 32¹⁰⁰⁰

5²⁰⁰⁰ = (5²)¹⁰⁰⁰ = 25¹⁰⁰⁰

Do 32 > 25 nên 32¹⁰⁰⁰ > 25¹⁰⁰⁰

Vậy 2⁵⁰⁰⁰ > 5²⁰⁰⁰

h) 6⁴⁵⁰ = (6³)¹⁵⁰ = 216¹⁵⁰

3⁷⁵⁰ = (3⁵)¹⁵⁰ = 243¹⁵⁰

Do 216 < 243 nên 216¹⁵⁰ < 243¹⁵⁰

Vậy 6⁴⁵⁰ < 3⁷⁵⁰

o) 333⁴⁴⁴ = (333⁴)¹¹¹ = [(3.111)⁴]¹¹¹ = (3⁴.111⁴)¹¹¹ = (81.111⁴)¹¹¹

444³³³ = (444³)¹¹¹ = [(4.111)³]¹¹¹

= (4³.111³)¹¹¹ = (64.111³)¹¹¹

Do 81 > 64 ⇒ 81.111⁴ > 64.111⁴ (1)

Do 4 > 3 ⇒ 64.111⁴ > 64.111³ (2)

Từ (1) và (2) ⇒ 81.111⁴ > 64.111³

⇒ (81.111⁴)¹¹¹ > (64.111³)¹¹¹

Vậy 333⁴⁴⁴ > 444³³³

2mũ 150 < 3 mũ 100

2¹⁵⁰= (2³)⁵⁰= 8⁵⁰

3¹⁰⁰= (3²)⁵⁰= 9⁵⁰

Vì 8⁵⁰< 9⁵⁰ nên 2¹⁵⁰ < 3¹⁰⁰

Vậy...

\(2^{150}< 3^{100}\)

chúc bạn học tốt!

\(-3^{150}=-9^{75}\)

\(-2^{225}=-8^{75}\)

mà -9<-8

nên \(-3^{150}< -2^{225}\)

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

a.ta có: \(3^{2009}\)

\(9^{1005}\)= \(\left(3^2\right)^{1005}\) =\(3^{2010}\)

*Vì 2010> 2009 =>\(3^{2009}\) < \(3^{2010}\)

Vậy \(3^{2009}\) < \(9^{1005}\).

2²²⁵ = (2³)⁷⁵ = 8⁷⁵ < 9⁷⁵ = (3²)⁷⁵ = 3¹⁵⁰

So sánh: 2²²⁵ và 3¹⁵⁰

2²²⁵=(2³)⁷⁵=8⁷⁵

3¹⁵⁰=(3²)⁷⁵=9⁷⁵

Vì 8⁷⁵ < 9⁷⁵

Nên 2²²⁵ < 3¹⁵⁰

\(-\left(-\dfrac{1}{16}\right)^{100}=-\left(-\dfrac{1}{2^4}\right)^{100}=-\left(\dfrac{1}{2^4}\right)^{100}=-\left[\left(\dfrac{1}{2}\right)^4\right]^{100}=-\left(\dfrac{1}{2}\right)^{400}=-\dfrac{1}{2^{400}}\)

\(-\left(-\dfrac{1}{8}\right)^{150}=-\left(-\dfrac{1}{2^3}\right)^{150}=-\left(\dfrac{1}{2^3}\right)^{150}=-\left[\left(\dfrac{1}{2}\right)^3\right]^{150}=-\left(\dfrac{1}{2}\right)^{450}=-\dfrac{1}{2^{450}}\)

\(\dfrac{1}{2^{400}}>\dfrac{1}{2^{450}}\Rightarrow-\dfrac{1}{2^{400}}< -\dfrac{1}{2^{450}}\)

Vậy \(-\left(-\dfrac{1}{6}\right)^{100}< -\left(-\dfrac{1}{8}\right)^{150}\)

a) 5¹⁴ = 5^2.7= (5²)⁷= 25⁷

3²¹= 3^3.7= (3³)⁷= 27⁷

Mà 25 < 27 

=> 5¹⁴<3²¹

b) 4³³= (4³)¹¹  = 64¹¹

3⁴⁴= (3⁴)¹¹ = 81¹¹

=> 4³³<3⁴⁴

c) 2¹⁶¹ > 2¹⁶⁰ = (2⁴)⁴⁰= 16⁴⁰

Mà 13⁴⁰< 16⁴⁰ < 2¹⁶¹

=> 13⁴⁰<2¹⁶¹

d) 17¹⁵= 17^3.5= (17³)⁵ = 4913⁵

31¹⁰= (31²)⁵= 961⁵

Mà 4913 > 961

=> 17¹⁵> 31¹⁰

e) 2²⁵⁵ = (2⁵)⁴⁵ = 32⁴⁵

3¹⁸⁰ = (3⁴)⁴⁵ = 81⁴⁵

=> 2²⁵⁵ < 3¹⁸⁰

g) 202³⁰³ = (202³)¹⁰¹ = (101³.2³)¹⁰¹= (101³.8)¹⁰¹= (101².8.101)¹⁰¹= (101².808)¹⁰¹

303²⁰² = (303²)¹⁰¹= (3².101²)¹⁰¹= (101².9) ¹⁰¹

Vì 101².9 < 101².808

=> 202³⁰³>303²⁰²