1.

a) 8⁵ = (2³)⁵ = 2¹⁵ = 2.2¹⁴

3.4⁷ = 3.(2²)⁷ = 3.2¹⁴

Do 2 < 3 nên 2.2¹⁴ < 3.2¹⁴

Vậy 8⁵ < 3.4⁷

b) Do 63 < 64 nên

63⁷ < 64⁷  (1)

Ta có:

64⁷ = (2⁶)⁷ = 2⁴²

16¹² = (2⁴)¹² = 2⁴⁸

Do 42 < 48 nên 2⁴² < 2⁴⁸

64⁷ < 16¹²  (2)

Từ (1) và (2) 63⁷ < 16¹²

c) Do 17 > 16 nên 17¹⁴ > 16¹⁴  (1)

Do 32 > 31 nên 32¹¹ > 31¹¹  (2)

Ta có:

16¹⁴ = (2⁴)¹⁴ = 2⁶⁴

32¹¹ = (2⁵)¹¹ = 2⁵⁵

Do 64 > 55 nên 2⁶⁴ > 2⁵⁵

16¹⁴ > 32¹¹  (3)

Từ (1), (2) và (3) 17¹⁴ > 31¹¹

d) Do 39 < 40 nên 3³⁹ < 3⁴⁰   (1)

Do 20 < 21 nên 11²⁰ < 11²¹   (2)

Ta có:

3⁴⁰ = (3²)²⁰ = 9²⁰

Do 9 < 11 nên 9²⁰ < 11²⁰   (3)

Từ (1), (2) và (3) 3³⁹ < 11²¹

e) Ta có:

72⁴⁵ - 72⁴⁴ = 72⁴⁴.(72 - 1) = 72⁴⁴.71

72⁴⁴ - 72⁴³ = 72⁴³.(72 - 1) = 72⁴³.71

Do 44 > 43 nên 72⁴⁴ > 72⁴³

72⁴⁴.71 > 72⁴³.71

Vậy 72⁴⁵ - 72⁴⁴ > 72⁴⁴ - 72⁴³

a) \(8^5=2^{15};3.4^7=3.2^{14}\) lớn hơn \(2^{15}\)

\(\Rightarrow8^5\) nhỏ hơn \(3.4^7\)

a: \(\frac{60}{72}=\frac{60:12}{72:12}=\frac56\)

\(\frac{24}{36}=\frac{24:12}{36:12}=\frac23=\frac{2\times2}{3\times2}=\frac46\)

mà 5>4

nên \(\frac{60}{72}>\frac{24}{36}\)

b: \(\frac{-13}{18}=\frac{-13\times2}{18\times2}=\frac{-26}{36}\)

\(\frac{-7}{12}=\frac{-7\times3}{12\times3}=\frac{-21}{36}\)

mà -26<-21

nên \(-\frac{13}{18}<-\frac{7}{12}\)

c: \(\frac{4}{15}=\frac{4\times6}{15\times6}=\frac{24}{90}\)

\(\frac{7}{18}=\frac{7\times5}{18\times5}=\frac{35}{90}\)

mà 24<35

nên \(\frac{4}{15}<\frac{7}{18}\)

d: \(\frac{123}{321}>0;0>-\frac{312}{213}\)

Do đó: \(\frac{123}{321}>-\frac{312}{213}\)

a: \(\frac{60}{72}=\frac{60:12}{72:12}=\frac56\)

\(\frac{24}{36}=\frac{24:12}{36:12}=\frac23=\frac{2\times2}{3\times2}=\frac46\)

mà 5>4

nên \(\frac{60}{72}>\frac{24}{36}\)

b: \(\frac{-13}{18}=\frac{-13\times2}{18\times2}=\frac{-26}{36}\)

\(\frac{-7}{12}=\frac{-7\times3}{12\times3}=\frac{-21}{36}\)

mà -26<-21

nên \(-\frac{13}{18}<-\frac{7}{12}\)

c: \(\frac{4}{15}=\frac{4\times6}{15\times6}=\frac{24}{90}\)

\(\frac{7}{18}=\frac{7\times5}{18\times5}=\frac{35}{90}\)

mà 24<35

nên \(\frac{4}{15}<\frac{7}{18}\)

d: \(\frac{123}{321}>0;0>-\frac{312}{213}\)

Do đó: \(\frac{123}{321}>-\frac{312}{213}\)

\(a=\left[\left(-\dfrac{1}{2}\right)^5\right]^{107}=\left(-\dfrac{1}{32}\right)^{107}\)

\(b=\left[\left(-\dfrac{1}{3}\right)^3\right]^{107}=\left(-\dfrac{1}{27}\right)^{107}\)

mà -1/32>-1/27

nên a>b

a>b

\(\frac{72}{167}>\frac{71}{169}\)

\(\frac{63}{314}< \frac{65}{321}\)

\(\frac{25}{101}< \frac{46}{180}\)

\(\frac{339}{322}\)và \(\frac{338}{321}\)

Ta có : \(\frac{339}{322}-1=\frac{17}{322};\frac{338}{321}-1=\frac{17}{321}\).

Vì \(\frac{17}{322}< \frac{17}{321}\)nên \(\frac{339}{322}< \frac{338}{321}\).

\(\frac{2017}{2014}\)và \(\frac{2018}{2015}\)

Ta có : \(\frac{2017}{2014}-1=\frac{3}{2014};\frac{2018}{2015}-1=\frac{3}{2015}\)

Vì \(\frac{3}{2014}>\frac{3}{2015}\)nên \(\frac{2017}{2014}>\frac{2018}{2015}\).

\(\frac{511}{514}\)và \(\frac{513}{516}\)

Ta có : \(1-\frac{511}{514}=\frac{3}{514};1-\frac{513}{516}=\frac{3}{516}\)

Vì \(\frac{3}{514}>\frac{3}{516}\)nên \(\frac{511}{514}< \frac{513}{516}\).

\(\frac{3005}{3000}\)và \(\frac{3010}{3005}\)

Ta có : \(\frac{3005}{3000}-1=\frac{5}{3000};\frac{3010}{3005}-1=\frac{5}{3005}\)

Vì \(\frac{5}{3000}>\frac{3}{3005}\)nên \(\frac{3005}{3000}>\frac{3010}{3005}\).

~ Chúc bn hok tốt ~

ta có: 3215/3216 <1

3104/3103>1

suy ra: 3215/3216 < 3104/3103

a) Ta có: \(\dfrac{34}{35}< 1;\dfrac{21}{20}>1\Rightarrow\dfrac{34}{35}< 1< \dfrac{21}{20}\)

Vậy \(\dfrac{34}{35}< \dfrac{21}{20}\)

a: \(\dfrac{34}{35}< 1< \dfrac{21}{20}\)

b: \(-\dfrac{123}{124}>-1>\dfrac{-321}{312}\)

c: \(\dfrac{1}{31}>\dfrac{1}{41}\)

\(\Leftrightarrow\dfrac{10}{31}+1>\dfrac{10}{41}+1\)

\(\Leftrightarrow\dfrac{41}{31}>\dfrac{51}{41}\)