a ) Ta có :  8¹⁵ = ( 2³ )¹⁵ = 2⁴⁵ = 2⁴² . 2³ = 2⁴² . 8

                 9. 4²¹ = 9. ( 2² ) ²¹ = 9. 2 ⁴² 

 Vì 8 < 9 nên 2⁴² .8 < 9. 2⁴²  hay 8¹⁵ < 9. 4²¹

                      Vậy 8¹⁵ < 9. 4²¹

 b) Ta có : 3²¹ = 3^{10.2 + 1} = 3¹⁰ . 3² + 3 = 3¹⁰ .9 + 3

               2³¹ = 2^10.3+1 = 2¹⁰.2³+2 = 2¹⁰ . 8 + 2

Vì 3 > 3 nên 3¹⁰ > 2¹⁰ ; 9> 8 ; 3 > 2 \(\Rightarrow\)3¹⁰.9 + 3 > 2¹⁰ .8 + 2 hay 3²¹ > 2³¹ 

                               Vậy 3^{21 >} 2³¹ 

Các bạn nhớ ****

viet cach lam luon nha

Ta có:\(2^{36}\)và \(3^{27}\)

\(2^{36}=\left(2^4\right)^9=16^9\)

\(3^{27}=\left(3^3\right)^9=27^9\)

Vì \(16< 27\Rightarrow16^9< 27^9\)

Vậy....

b,\(9^{20}\)và \(9999^{10}\)

\(9^{20}=\left(9^2\right)^{10}=81^{10}\)

\(9999^{10}\)

Vì \(81< 9999\Rightarrow81^{10}< 9999^{10}\)

Vậy ...

c,\(54^4\)

\(21^{12}=\left(21^3\right)^4=9261^4\)

Vì \(54< 9261\Rightarrow54^4< 9261^4\)

Vậy...

cam on

2^70<3^51

3^10<2^21

2^70 va 3^51

vi 3^51>3^50 ma 3^50=(3^5)^10=243^10

                             2^70=(2^7)10=128^10

=>3^50>2^70

vi 3^51>3^50 nen 3^51>2^70

cau tiep theo lam tuong tu nhe!

(xin loi may tinh cua minh khong danh duoc dau)

luc do minh khong biet lam nhung co giao minh chua nen minh giai de cho cac ban biet cach lam dung hieu nham minh nhe

\(99^{20}< 9999^{10}\)

\(54^4< 21^{12}\)

\(71^5< 17^{20}\)

\(2^{30}+3^{20}+4^{30}>3\times24^{10}\)
 

a) \(21^{15}=21^{3.5}=\left(21^3\right)^5=9261^5\)

Vì \(9261>27\Rightarrow9261^5>27^5\Rightarrow21^{15}>27^5\)

b) \(15^{12}=\left(3.5\right)^{12}=3^{12}.5^{12}\)

\(81^3.125^5=\left(3^4\right)^3.\left(5^3\right)^5=3^{4.3}.5^{3.5}=3^{12}.5^{15}\)

Vì \(3^{12}=3^{12}\)mà \(5^{12}< 5^{15}\Rightarrow3^{12}.5^{12}< 3^{12}.5^{15}\Rightarrow15^{12}< 81^3.125^5\)

Ta có: 2/3= 2000/3000 ; 21/31= 2100/3100 ; 211/311= 2110/ 3110

Lại có:   2000/3000 = 1-1000/3000 ;  2100/3100= 1-1000/3100

             2110/3110 = 1-1000/3110 ;  2112/3112= 1-1000/3112

mà 1000/3000>1000/3100>1000/3110>1000/3112

=> Thứ tự đúng là 2000/3000<2100/3100<2110/3110<2112/3112

=> 2/3<21/31<211/311<2112/3112

2⁹¹<5³⁵

54⁴<21¹²

ta có 
2⁹¹=(2¹³)⁷=8192⁷
5³⁵=(5⁵)⁷=3125⁷
Vì 8192⁷>3125⁷=>2⁹¹>5³⁵

 

Ta có
54⁴=(2.27)⁴=(2.3³)⁴=2⁴.3¹²
21¹²=(3.7)¹²=3¹².7¹²
7¹²=(7³)⁴=343⁴
Vì 343⁴>2⁴<=>7¹²>2⁴
mà 3¹²=3¹²=>54⁴<21¹²