a) Vì \(-45< -16\) nên \(\left(-\dfrac{45}{17}\right)^{15}< \left(\dfrac{-16}{17}\right)^{15}\)

b) Vì \(21< 23\) nên \(\left(-\dfrac{8}{9}\right)^{21}< \left(-\dfrac{8}{9}\right)^{23}\)

c) \(27^{40}=3^{3^{40}}=3^{120}\)

\(64^{60}=8^{2^{60}}=8^{120}\)

Vì \(3< 8\) nên \(3^{120}< 8^{120}\) hay \(27^{40}< 64^{60}\)

a)\(\frac{14}{15}\) < \(\frac{15}{21}\)

b)\(\frac{101}{200}\) < \(\frac{200}{404}\)

c)\(\frac{1995}{2011}\) >\(\frac{1993}{2012}\)

\(\frac{75}{100}=\frac{3}{4}=\frac{6}{8}< \frac{7}{8}\)

\(\frac{7}{8}< 1< \frac{3}{2}\)

\(\frac{60}{108}=\frac{5}{9}=\frac{15}{27}>\frac{15}{37}\)

\(\frac{15}{37}=\frac{30}{74}< \frac{31}{74}< \frac{31}{54}\)

\(\frac{0}{16}=\frac{0}{21}\)

Xét \(1-\frac{1965}{1967}=\frac{2}{1967}>\frac{2}{1975}=1-\frac{1973}{1975}\Rightarrow\frac{1965}{1967}< \frac{1973}{1975}\)

\(a.\dfrac{5}{10}=\dfrac{1}{2}=\dfrac{1\times3}{2\times3}=\dfrac{3}{6}\)

\(\dfrac{25}{75}=\dfrac{1}{3}=\dfrac{1\times2}{3\times2}=\dfrac{2}{6}\)

\(b.\dfrac{42}{56}=\dfrac{3}{4}=\dfrac{3\times2}{4\times2}=\dfrac{6}{8}\)

\(\dfrac{18}{48}=\dfrac{3}{8}\)

\(c.\dfrac{27}{81}=\dfrac{1}{3}=\dfrac{1\times4}{3\times4}=\dfrac{4}{12}\)

\(\dfrac{57}{76}=\dfrac{3}{4}=\dfrac{3\times3}{4\times3}=\dfrac{9}{12}\)

\(\dfrac{35}{84}=\dfrac{5}{12}\)

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a.3/6 va 2/6     b.24/32 va12/32  c.912/2736  2052/2736 1140/2736 

A) Ta có: 

\(\dfrac{12}{13}=\dfrac{13}{13}-\dfrac{1}{13}=1-\dfrac{1}{13}\)

\(\dfrac{13}{14}=\dfrac{14}{14}-\dfrac{1}{14}=1-\dfrac{1}{14}\)

Mà \(1-\dfrac{1}{13}< -\dfrac{1}{14}\)

\(\Rightarrow\dfrac{12}{13}< \dfrac{13}{14}\)

B) Ta có:

\(\dfrac{125}{251}=\dfrac{251}{251}-\dfrac{126}{251}=1-\dfrac{126}{251}\)

\(\dfrac{127}{253}=\dfrac{253}{253}-\dfrac{126}{253}=1-\dfrac{126}{253}\)

Mà: \(1-\dfrac{126}{251}< 1-\dfrac{126}{253}\)

\(\Rightarrow\dfrac{125}{251}< \dfrac{127}{253}\)

a)\(3^{75}=3^{25.3}=\left(3^3\right)^{25}=27^{25}\)

\(4^{50}=4^{25.2}=\left(4^2\right)^{25}=16^{25}\)

Ta có 2 kết quả trên cùng số mũ mà:27>16.

Vậy \(3^{75}>4^{50}\)

b)\(2^{31}< 2^{32}=2^{4.8}=\left(2^4\right)^8=16^8\)

\(3^{21}=3^{7.3}=\left(3^3\right)^7=27^7\)

\(3^{21}=27^7>16^8>2^{31}\)

Vậy \(3^{21}>2^{31}\)

Chúc em học tốt^^

Cảm ơn bạn nhé!

ta có:19/20<20/20 và 20/20<20/21

ta có:1-17/21=21/21-17/21=4/21 

                                               nên 4/21>4/27

         1-23/27=27/27=4/27

ta có:31/29-1=31/29-29/29=2/29

                                                nên 31/29>45/43

        45/43-1=43/43-45/43=2/43

nhớ k mình nha

a: 3>2

=>5/3<5/2

b: 23/21>1

21/23<1

=>23/21>21/23

c: -15/-17>0

16/-19<0

=>-15/-17>16/-19

-251/138 > -317/171

tick đi mik giải thích cho