Câu c:

10^30 và 2^100

10^30 = (10^3)^10 = 1000^10

2^100 = (2^10)^10 = 2024^10 > 1000^10

2^100 > 10^30

333^444 = (333^4)^111

444^333 = (444^3)^111

333^4 = 3^4.111^4 = 81.111^4

444^3 = 4^3.111^3 = 64.111^3 < 81.111^4

444^3< 333^4

(333^4)^111 > (444^3)^111

333^444 > 444^333

Câu 2:

5^300 và 3^453

5^300 = (5^2)^150 = 25^150

3^453 > 3^450 = (3^3)^150 = 27^150

25^150 < 27^150

Vậy 5^300 < 3^453

Câu 3:

333^444 = (333^4)^111

444^333 = (444^3)^111

333^4 = 3^4.111^4 = 81.111^4

444^3 = 4^3.111^3 = 64.111^3 < 81.111^4

444^3< 333^4

(333^4)^111 > (444^3)^111

333^444 > 444^333

10³⁰= (10³)¹⁰= 1000¹⁰

2¹⁰⁰=(2¹⁰)¹⁰=1024¹⁰

1000<1024 =>1000¹⁰<1024¹⁰ nên 10³⁰<2¹⁰⁰

Câu b:

333^444 = (333^4)^111

444^333 = (444^3)^111

333^4 = 3^4.111^4 = 81.111^4

444^3 = 4^3.111^3 = 64.111^3 < 81.111^4

444^3< 333^4

(333^4)^111 > (444^3)^111

333^444 > 444^333

a)Ta có: \(2^{161}>2^{160}\)

Mà \(2^{160}=2^{4.40}=\left(2^4\right)^{40}=16^{40}\)

=> \(2^{161}>16^{40}\)                                       (1)

Mà \(16^{40}>13^{40}\)(Vì 16>13)                       (2)

Từ (1)và(2)=> \(2^{161}>16^{40}>13^{40}\)

                Vậy \(2^{161}>13^{40}\)

b)Ta có :+) \(3^{453}>3^{450}\)

Mà \(3^{450}=3^{3.150}=\left(3^3\right)^{150}=27^{150}\)

=> \(3^{453}>27^{150}\)                                                            (1)

              +)\(5^{300}=5^{2.150}=\left(5^2\right)^{150}=25^{150}\)       (2)

               Mà \(27^{150}>25^{150}\)( Vì 27>25)                          (3)

Từ (1);(2)và(3)=> \(3^{453}>27^{150}>25^{150}\)

                        Hay \(3^{453}>5^{300}\)

                              Vậy \(3^{453}>5^{300}\)

Chú ý: Dấu "." là nhân nha!!!

          Nhớ bấm "Đúng" cho mình nha!!!

Câu a:

10^30 và 2^100

(10^3)^10 = 1000^10

2^100 = (2^10)^10 = 1024^10 > 1000^10

Vậy 10^30 < 2^100

333^444 = (333^4)^111

444^333 = (444^3)^111

333^4 = 3^4.111^4 = 81.111^4

444^3 = 4^3.111^3 = 64.111^3 < 81.111^4

444^3< 333^4

(333^4)^111 > (444^3)^111

333^444 > 444^333

Ta có: 333⁴⁴⁴=333^111.4=333⁴mũ 111=12296370321¹¹¹

              444³³³=444^111.3=444³mũ 111=87528384¹¹¹

Mà: 12296370321>87528384 và 111=111.

=>333⁴⁴⁴>444³³³.

Tk phát nhé

333^444 = (333^4)^111

444^333 = (444^3)^111

333^4 = 3^4.111^4 = 81.111^4

444^3 = 4^3.111^3 = 64.111^3 < 81.111^4

444^3< 333^4

(333^4)^111 > (444^3)^111

333^444 > 444^333

a, 2^100

b, 333^444

c,2^161

d, 3^453

a) Ta có : \(10^{30}=\left(10^3\right)^{10}=1000^{10}\)

                  \(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

mà \(1000< 1024\)

\(\Rightarrow1000^{10}< 1024^{10}\)

\(\Rightarrow10^{30}< 2^{100}\)

b) Ta có : \(333^{444}=\left(111.3\right)^{444}=111^{444}.3^{444}=111^{444}.\left(3^4\right)^{111}=111^{444}.81^{111}\)

                 \(444^{333}=\left(111.4\right)^{333}=111^{333}.4^{333}=111^{333}.\left(4^3\right)^{111}=111^{333}.64^{111}\)

mà \(444>333\Rightarrow111^{444}>111^{333}\)

và \(81>64\Rightarrow81^{111}>64^{111}\)

\(\Rightarrow111^{444}.81^{111}>111^{333}.64^{111}\)

\(\Rightarrow333^{444}>444^{333}\)

c) Ta có : \(2^{161}>2^{160}=\left(2^4\right)^{40}=16^{40}>13^{40}\)

\(\Rightarrow2^{161}>13^{40}\)

d) Ta có : \(3^{453}>3^{450}=\left(3^3\right)^{150}=27^{150}>25^{150}=\left(5^2\right)^{150}=5^{300}\)

\(\Rightarrow3^{453}>5^{300}\)

\(333^{444}=\left(333\times4\right)^{111}=1332^{111}\)

\(444^{333}=\left(444\times3\right)^{111}=1332^{111}\)

\(1332^{111}=1332^{111}\Rightarrow333^{444}=444^{333}\)

\(333^{444}=\left(333^4\right)^{111}\)

\(444^{333}=\left(444^3\right)^{111}\)

\(\Rightarrow333^4=111^4.3^4=111^3.111.3^4\)

     \(444^3=111^3.4^3\)

\(\Rightarrow111.3^4=111.81>4^3=64\)

\(\Rightarrow333^{444}>444^{333}\)

a: 10^30=1000^10

2^100=1024^10

=>10^30<2^100

h: \(2^{91}=8192^7\)

5^35=3125^7

=>2^91>5^35

c: 19^20=2476099^4

9^8=81^4

=>19^20>9^8

d: 107^50=11449^25

73^75=389017^25

=>107^50<73^75