\(26^{14}>25^{14}=\left(5^2\right)^{14}=5^{28}\)

\(5^{30}=\left(5^3\right)^{10}=125^{10}>124^{10}\)

\(4^{21}=\left(4^3\right)^7=64^7>64^2\)

\(27^{16}.16^9=\left(3^3\right)^{16}.\left(4^2\right)^9=3^{48}.4^{18}>12^{18}=3^{18}.4^{18}\)

\(31^{11}16^{14}=\left(2^4\right)^{14}=2^{56}\)

\(2^{56}>2^{55}\) => \(17^{14}>31^{11}\)

Các bài khác làm tương tự

a, Có 5^28 = (5^2) ^14

                =25^14 < 26^14 

b, Có 5^30 = (5^3) ^10)

                =125^10 > 124^10

ý cậu là 107 mũ 50 và 73 mũ 75 hả

a. \(107^{50}< 73^{75}\)

b. \(54^4< 21^{12}\)

c. \(2^{91}>5^{35}\)

d. \(3^{500}>7^{300}\)

e. \(122^{26}< 10^{51}\)

g. \(124^{30}>625^{23}\)

a)\(\frac{7}{8}\)  và  \(\frac{8}{7}\)

 - Phân số \(\frac{7}{8}\) là phân số bé hơn 1,phân số \(\frac{8}{7}\) lại là phân số lớn hơn 1 cho nên \(\frac{7}{8}\) < \(\frac{8}{7}\)

 -Quy đồng mẫu số hai phân số: \(\frac{7}{8}\) = \(\frac{49}{56}\)              \(\frac{8}{7}\)  = \(\frac{64}{56}\)   => \(\frac{7}{8}\) <  \(\frac{8}{7}\)

a,>

b,>

c,>

d,>

e,>

g,>

a) Ta có:

+) \(\dfrac{1}{2}=\dfrac{3}{6}\)

+) \(\dfrac{1}{3}=\dfrac{2}{6}\)

+) \(\dfrac{2}{3}=\dfrac{4}{6}\)

=> \(\dfrac{2}{6}< \dfrac{3}{6}< \dfrac{4}{6}\)

hay \(\dfrac{1}{3}< \dfrac{1}{2}< \dfrac{2}{3}\)

b) Ta có:

+) \(\dfrac{4}{9}=\dfrac{56}{126}\)

+) \(-\dfrac{1}{2}=-\dfrac{63}{126}\)

+) \(\dfrac{3}{7}=\dfrac{54}{126}\)

=> \(-\dfrac{63}{126}< \dfrac{54}{126}< \dfrac{56}{126}\)

hay \(-\dfrac{1}{2}< \dfrac{3}{7}< \dfrac{4}{9}\)

c) Ta có:

+) \(\dfrac{27}{82}=\dfrac{2025}{6150}\)

+) \(\dfrac{26}{75}=\dfrac{2132}{6150}\)

=> \(\dfrac{2025}{6150}< \dfrac{2132}{6150}\)

hay \(\dfrac{27}{82}< \dfrac{26}{75}\)

d) Ta có:

+) \(-\dfrac{49}{78}=-\dfrac{4655}{7410}\)

+) \(-\dfrac{64}{95}=-\dfrac{4992}{7410}\)

=> \(-\dfrac{4665}{7410}>-\dfrac{4992}{7410}\)

hay \(-\dfrac{49}{78}>-\dfrac{64}{95}\)