9⁹⁹ > 99⁹

OK

a, Ta có : \(9^{2000}=\left(3^2\right)^{2000}=3^{4000}\)

Mà \(3^{4000}=3^{4000}\)

\(\Rightarrow3^{4000}=9^{2000}\)

Vậy \(3^{4000}=9^{2000}\)

b, Ta có : \(2^{332}< 2^{333}=2^{3.111}=\left(2^3\right)^{111}=8^{111}\)

\(3^{223}>3^{222}=3^{2.111}=\left(3^2\right)^{111}=9^{111}\)

Vì \(8^{111}< 9^{111}\)

\(\Rightarrow2^{333} < 3^{222}\)

\(\Rightarrow2^{332}< 3^{223}\)

Vậy \(2^{332}< 3^{223}\)

a) \(3^{4000}\) và \(9^{2000}\)

ta có:\(9^{2000}=\left(3^2\right)^{2000}=9^{2000}\)

=>\(9^{2000}=9^{2000}\Leftrightarrow3^{4000}=9^{2000}\)

b)\(2^{332}\) và \(3^{223}\)

\(2^{332}\) <\(2^{333}\) mà \(2^{333}=\left(2^3\right)^{111}=8^{111}\)(1)

\(3^{223}\) >\(3^{222}\) mà \(3^{222}=\left(3^2\right)^{111}=9^{111}\)(2)

từ (1 và 2),suy ra:8¹¹¹<9¹¹¹ hay 2³³²<3²²³

2/5 x 1/X + 1/X x 2 = 0,1

1/X x ( 2/5 + 2 ) = 0,1

1/X x 12 / 5 = 0,1

1/X             = 0,1 :12/5 = 1/10 : 12/5

1/X             = 1/24

Vậy X = 24

\(123456789^9\) < \(9^{123456789}\)

\(\frac{-4}{3}=\frac{-28}{21};\frac{9}{-7}=\frac{-27}{21}\Rightarrow\frac{-4}{3}

Ta có: 81^11 = ( 9^2 )^11 = 9^22

Vì 9^28 > 9^22

=> 9^28 > 81^11

\(81^{11}=\left(9^2\right)^{^{11}}=9^{2.11}=9^{22}< 9^{28}\)

Vậy \(9^{28}>81^{11}\)

2 ngũ 6 nhân 3 mũ 3 = 64 x 27 = 1728

27^3>9^4

A = 387420490 ; B = 1000000001

vậy B lớn hơn A