Ta có 31^11<32^11=(2^5)^11=2^55 

Suy ra: 31^11<2^55

17^14>16^14=(2^4)^14=2^56

Suy ra: 17^14>2^56

Mặt khác: 31^11<2^55<2^56<17^14

nên 31^11<17^14

a)16¹⁹<8¹⁵

b)27¹¹<81⁸

\(a)16^{19}=\left(8\times2\right)^{19}=8^{19}\times2^{19}>8^{19}>8^{15}\)

\(\Rightarrow16^{19}>8^{15}\)

\(b)81^8=\left(3^4\right)^8=3^{24}< 3^{33}=\left(3^3\right)^{11}=27^{11}\)

\(\Rightarrow27^{11}>81^8\)

\(c)625^5=\left(5^4\right)^5=5^{20}< 5^{21}=\left(5^3\right)^7=125^7\)

\(\Rightarrow125^7>625^5\)

\(d)244^{11}>243^{11}=\left(3^5\right)^{11}=3^{55}>3^{52}=\left(3^4\right)^{13}=81^{13}>80^{13}\)

\(\Rightarrow244^{11}>80^{13}\)

\(d)31^{17}>17^{17}>17^{14}\)

\(\Rightarrow31^{17}>17^{14}\)

Bài 31 :

a ) 31¹¹ < 17¹⁴

b ) 65⁷ > 4²¹

Bài 32 : 

Bài 31 :

a) 31¹¹ < 17¹⁴

b) 65⁷ > 4²¹

a) ta có

\(\left\{{}\begin{matrix}199^{20}=\left(199^4\right)^5=1568239201^5\\2003^{15}=\left(2003^3\right)^5=80360540276^5\end{matrix}\right.\)

vì 1568239201 < 80360540276 ⇒ 199²⁰<2003¹⁵

^{các câu khác làm tương tự}

\(\frac{15}{29}+\frac{-9}{31}+\frac{-7}{8}+\frac{14}{29}-\frac{-22}{31}=\frac{15}{29}+\frac{14}{29}+\left(\frac{-9}{31}+\frac{-22}{31}\right)-\frac{-7}{8}=0-\frac{-7}{8}=\frac{7}{8}\)

có duyên ghê taaaaaaaaaaaaaaaaaaaaaa............

Duyên j cơ, bn ko trả lời thì ra chỗ khác đi

\(a,(\frac{1}{4}+\frac{-5}{13})+(\frac{2}{11}+\frac{-8}{13}+\frac{3}{4})\)

\(= (\frac{1}{4} + \frac{3}{4}) + (\frac{-5}{13} + \frac{-8}{13}) + \frac{2}{11}\)

\(= \frac{4}{4} + \frac{-13}{13} + \frac{2}{11}\)

\(=1+(-1)+\frac{2}{11}=\frac{2}{11}\)

\(b,(\frac{21}{31}+\frac{-16}{7})+(\frac{44}{53}+\frac{10}{31})+\frac{9}{53}\)

\(= (\frac{21}{31} + \frac{10}{31}) + (\frac{44}{53} + \frac{9}{53}) + \frac{-16}{7}\)

\(=\frac{31}{31}+\frac{53}{53}+\frac{-16}{7}=1+1-\frac{16}{7}\)

\(=2-\frac{16}{7}=\frac{14}{7}-\frac{16}{7}=-\frac27\)

\(c,\frac{-5}{7}+\frac{3}{4}+\frac{-1}{5}+\frac{-2}{7}+\frac{1}{4}\)

\(= (\frac{-5}{7} + \frac{-2}{7}) + (\frac{3}{4} + \frac{1}{4}) + \frac{-1}{5}\)

\(= \frac{-7}{7} + \frac{4}{4} + \frac{-1}{5}\)

\(=-1+1-\frac{1}{5}=0-\frac15=-\frac15\)

\(\frac{-3}{31} + \frac{-6}{17} + \frac{1}{25} + \frac{-28}{31} + \frac{-11}{17} + \frac{-1}{5}\)

\(= (\frac{-3}{31} + \frac{-28}{31}) + (\frac{-6}{17} + \frac{-11}{17}) + \frac{1}{25} + \frac{-1}{5}\)

\(= \frac{-31}{31} + \frac{-17}{17} + \frac{1}{25} - \frac{5}{25}\)

\(= -1 + (-1) + \frac{-4}{25}\)

\(=-2-\frac{4}{25}=-\frac{50}{25}-\frac{4}{25}=-\frac{54}{25}\)

\(\frac{-7}{31}\) và \(\frac{6}{31}\)

\(\frac{-7}{31}<0;\frac{6}{31}>0\)

=>\(-\frac{7}{31}<\frac{6}{31}\)

\(\frac{-97}{128}\) và \(-\frac{99}{128}\)

vì \(\frac{97}{128}<\frac{99}{128}\) =>\(\frac{-97}{128}>-\frac{99}{128}\)

\(\frac37\) và \(\frac{-6}{7}\)

vì\(\frac37>0;-\frac67<0\)

=>\(\frac37>-\frac67\)