ta có : 52/91=4/7

60/84=5/7

Vì mẫu 2 phân số trên bằng nhau, 4<5 nên 4/7<5/7

hay 52/91<60/84

Vậy  ....

52/91=4/7(1)

60/84=4/7(2)

Từ (1) và (2) => 52/91=60/84

A>B

A > B

?

ta có: 2⁷ > 2⁶ = (2³)² = 8² > 7²

=> 2⁷ > 7²

#

Ta có :

2⁷= 128

7² = 49 

=> 2⁷>7²

A- 1 = \(\frac{10^{2015}-1-\left(10^{2016}-1\right)}{10^{2016}-1}=\frac{-9.10^{2015}}{10^{2016}-1}=\frac{-90.10^{2014}}{10^{2016}-1};\)

B- 1 = \(\frac{10^{2014}+1-\left(10^{2015}+1\right)}{10^{2015}+1}=\frac{-9.10^{2014}}{10^{2015}+1};\)

xét \(\frac{A-1}{B-1}=\frac{-90.10^{2014}}{10^{2016}-1}:\frac{-9.10^{2014}}{10^{2015}+1}=\frac{10\left(10^{2015}+1\right)}{10^{2016}-1}=\frac{10^{2016}+10}{10^{2016}-1}>1\)

=> A-1 > B-1 => A > B

TL

2¹⁶¹ = (2⁴)^{161 / 4} = 16^{161 / 4}

So sánh : 13 < 16 ; 40 < 161 / 4 ( = 40, 25 )

=> 13⁴⁰ < 2¹⁶¹

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2017^10+2017^9=2017^9+(1+2017)=2017^9x2018

2018^10=2018^9+2018

ta có:2018=2018

2017^9<2018^9

=>2017^10+2017^9<2018^10

\(\dfrac{7^{45}}{7}=7^{44}\)

\(49.7^{20}=7^2.7^{20}=7^{22}\)

\(\Rightarrow\dfrac{7^{45}}{7}=7^{44}>7^{22}=49.7^{20}\)

7⁴⁵ : 7 ²³ =  7²² 

49 \(\times\) 7²⁰ = 7² \(\times\) 7²⁰ = 7²²

7⁴⁵ : 7²³ = 49 \(\times\) 7²⁰