B

B

B

a) 2 3  = 8 ; 3 2  = 9

Vì 8 < 9 nên  2 3  <  3 2

a. \(\dfrac{10}{21}>1\)

\(\dfrac{9}{23}< 1\)

\(\Rightarrow\dfrac{10}{21}>\dfrac{9}{23}\)

b. \(\dfrac{32}{33}>\dfrac{31}{33}>\dfrac{31}{34}\Rightarrow\dfrac{32}{33}>\dfrac{31}{34}\)

c. \(\dfrac{44}{47}< \dfrac{45}{47}< \dfrac{45}{46}\Rightarrow\dfrac{44}{47}< \dfrac{45}{46}\)

\(d.\dfrac{70}{117}< \dfrac{70}{115}=\dfrac{14}{23}\Rightarrow\dfrac{70}{117}< \dfrac{14}{23}< \dfrac{15}{23}\)

\(\Rightarrow\dfrac{70}{117}< \dfrac{15}{23}\)

Chọn A

A

A

a)  3 2 = 9 6 ; 2 3 = 4 6 . Do  9 6 > 4 6 > 1 6 ⇒ 3 2 > 2 3 > 1 6

b)  13 57 = 26 114 ; 29 38 = 87 114 . Do  26 114 < 87 114 ⇒ 13 57 < 29 38

`A=4(3^2+1)(3^4+1)...(3^64+1)`

`=>2A=(3^2-1)(3^2+1)(3^4+1)...(3^64+1)`

- Ta có: 

`(3^2-1)(3^2+1)=3^4-1`

`(3^4-1)(3^4+1)=3^16-1`

`....`

`(3^64-1)(3^64+1)=3^128-1`

Suy ra `2A=3^128-1=B`

`=>A<B`

Bài làm:

Ta có: \(\left(-32\right)^9=-2^{45}=-2^{13}.2^{32}\)

\(\left(-18\right)^{13}=-2^{13}.3^{26}\)

Mà \(3^{26}>3^{24}=27^8>16^8=2^{32}\)

=> \(-2^{13}.2^{32}>-2^{13}.3^{26}\)

=> \(\left(-32\right)^9>\left(-18\right)^{13}\)

Ta có : \(18^{13}>16^{13}=\left(2^4\right)^{13}=2^{52}\)

             \(32^9=\left(2^5\right)^9=2^{45}\)

mà 52 > 45

\(\Rightarrow2^{52}>2^{45}\)

\(\Rightarrow18^{13}>32^9\)

\(\Rightarrow\left(-18\right)^{13}< \left(-32\right)^9\)