a)Ta có :27¹¹ = (3³)¹¹ = 3^3.11 = 3³³

              81⁸ = (3⁴)⁸ = 3^4.8 = 3³²

Vì 3³³ > 3³² nên 27¹¹ > 81⁸

b) Ta có : 3³⁹ = 3^3.13 = (3³)¹³ = 27¹³

                11²⁶ = 11^2.13 = (11²)¹³ = 121¹³

Vì 27 < 121 nên 27¹³ < 121¹³ nên 3³⁹ < 11²⁶

1) 27¹¹ và 81⁸

Ta có : 27¹¹ = (3³)¹¹ =3³³ ; 81⁸ = (3⁴)⁸ = 3³²

Vì 3³³ > 3³² nên 27¹¹ > 81⁸

2) 3³⁹ và 11²⁶

Ta có : 3³⁹ = (3³)¹³ = 27¹³ ; 11²⁶ = (11²)¹³ = 121¹³

Vì 27¹³ < 121¹³ nên 3³⁹ < 11²⁶

=))

\(a,\)\(27^{11}\)và \(81^8\)

Ta có: \(27^{11}=\left(3^3\right)^{11}=3^{3.11}=3^{33}\)

\(81^8=\left(3^4\right)^8=3^{4.8}=3^{32}\)

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

\(b,\)\(3^{39}\)và \(11^{26}\)

Ta có: \(3^{39}=3^{3.13}=\left(3^3\right)^{13}=27^{13}\)

\(11^{26}=11^{2.13}=\left(11^2\right)^{13}=121^{13}\)

Vì: \(27^{13}< 121^{13}\)nên \(3^{39}< 11^{26}\)

~ Rất vui vì giúp đc bn ~

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

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

\(125^{12}>121^{12}\Rightarrow5^{36}>11^{24}\)

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

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

Vì 121¹² < 125¹²

Nên 11²⁴ < 5³⁶

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

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

Vì \(125^{12}>121^{12}\Rightarrow5^{36}>11^{24}\)

T.I.C.K GIÚP MK NHÉ!

17¹⁵ và 2⁵⁹

ta có:

17¹⁵>16¹⁵ ; 16¹⁵= (2⁴)¹⁵=2⁶⁰

Vì 2⁶⁰> 2⁵⁹=>16¹⁵>2⁵⁹

=>17¹⁵>2⁵⁹

\(8^5=\left(2^3\right)^5=2^{15}=2.2^{14}\)

\(3.4^7=3.\left(2^2\right)^7=3.2^{14}\)

Vì 2 < 3 nên 8⁵ < 3 . 4⁷

8^5<3.4^7

Câu 1: 3^23  >    5^12

Câu 2: 3^36 < 2^8.11^4

2¹⁵⁶=2^4*39=(2⁴)³⁹=16³⁹

Vì 18>16 nên 18³⁹>16³⁹ hay 18³⁹>2¹⁵⁶

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

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

\(32^n>25^n\Rightarrow2^{5n}>5^{2n}\)

Vậy ........

Chúc em học tốt^^

ta c0:

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

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

vj 32>25\(\Rightarrow32^n>25^n\)

hay  \(2^{5n}>5^{2n}\)

Theo bai ra , ta co:

2⁵ⁿ=(2⁵)ⁿ=10ⁿ va 5²ⁿ=(5²)ⁿ=10ⁿ

Do 10ⁿ = 10ⁿ =>2⁵ⁿ = 5²ⁿ voi moi n thuoc Z

Bài 1:

a, \(64^2=\left(2^6\right)^2=2^{12}\)

\(32^5=\left(2^5\right)^5=2^{25}\)

\(2^{12}< 2^{25}\Rightarrow64^2< 32^5\)

b, \(10^5=\left(5.2\right)^5=5^5.2^5\)

\(5^{10}=5^{5+5}=5^5.5^5\)

\(5^5.2^5< 5^5.5^5\Rightarrow10^5< 5^{10}\)

c, 256^ mấy thế hả bạn?

d, \(9^{200}=\left(9^2\right)^{100}=81^{100}\)

\(81^{100}>10^{100}\Rightarrow9^{200}>10^{100}\)

Bài 2:

\(9.27^2.81^3.216\)

\(=3^2.\left(3^3\right)^2.\left(3^4\right)^3.2^3.3^3\)

\(=3^2.3^6.3^{12}.3^3.2^3\)

\(=3^{2+6+12+3}.2^3\)

\(=3^{23}.2^3\)