32^50=(2^5)^50

27^57=2^

2¹⁵⁶=2^4*39=(2⁴)³⁹=16³⁹

Vì 18>16 nên 18³⁹>16³⁹ hay 18³⁹>2¹⁵⁶

a/

\(27^{81}=\left(3^3\right)^{81}=3^{241}\)

\(81^{27}=\left(3^4\right)^{27}=3^{108}\)

\(\Rightarrow27^{81}=3^{241}>3^{108}=81^{27}\)

b/

\(5^{60}=\left(5^3\right)^{20}=125^{20}\)

\(7^{40}=\left(7^2\right)^{20}=49^{20}\)

\(\Rightarrow5^{60}=125^{20}>49^{20}=7^{40}\)

c/

\(11^{102}=\left(11^2\right)^{51}=121^{51}>121^{50}>99^{50}\)

a) \(32^{50}\)và \(27^{51}\)

\(32^{50}=\left(32^2\right)^{25}=1024^{25}\)

\(27^{51}=\left(27^2\right)^{25}.27=729^{25}.27\)

Vì \(1024>729\)nên \(1024^{25}>729^{25}.27\)hay \(32^{50}>27^{51}\)

b) \(31^9\)và \(9^{16}\)

\(31^9=\left(91^3\right)^2=273^2\)

\(9^{16}=\left(9^2\right)^4=81^4=\left(81^2\right)^2=6561^2\)

Vì \(6561>273\)nên \(273^2< 6561^2\)hay \(31^9< 9^{16}\).

câu 1 sai đề r bn 81⁸ ko pk 8¹⁸

1) \(27^{11}=\left(3^3\right)^{11}=3^{33}\)

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

\(33>32\Rightarrow3^{33}>3^{32}\Rightarrow27^{11}>81^8\)

\(21^{15}=\)6,812231858_x10¹⁹

\(27^5.49^8=\)4,768562301_x10¹²

nen \(21^{15}< 27^5.49^8\)

ta có \(21^{15}=\left(3.7\right)^{15}=3^{15}.7^{15}\)

\(27^5.49^8=3^{15}.7^{16}\)

Mà \(7^{15}< 7^{16}\Rightarrow21^{15}< 27^5.49^8\)

21¹⁵ = ( 3 . 7 )¹⁵ = 3¹⁵ . 7¹⁵

27⁵ . 49⁸ = 9¹⁵ . 7¹⁶

Vì 9¹⁵ > 3¹⁵ ; 7¹⁶ >  7¹⁵

=> 21¹⁵ < 27⁵ . 49⁸

ta có 31^11 < 32^11 và 17^14 . 16^14

nên ta có 32^11 = (2^5)^11 = 2^55

             16^14=(2^4)^14=2^56

ta thấy 55<56

suy ra 2^55 <2^56

suy ra 32^11<16^14

tức 31^11<17^14

K CHO MINH ĐI , HÔM SAU CÓ BÀI GÌ MÌNH GIẢI CHO

4⁵⁰=  ( 4³ ) ^50/3 = 64 ^50/3

8³⁰ =( 8² ) ¹⁵ = 64¹⁵

ta có 50/3 > 15 => 4⁵⁰ > 8³⁰

\(4^{50}\)= \(\left(2^2\right)^{^{50}^{ }}\)\(=2^{100}\)

\(8^{30}=\left(2^3\right)^{30}=2^{90}\)

vì \(2^{100}>2^{90}\)nên\(4^{50}>8^{30}\)