\(5^{23}\)=     \(5\cdot5^{22}\)<     \(6\cdot5^{22}\)

5²³ < 6.5²²

72⁴⁵ - 72⁴⁴ > 72⁴⁴ - 72⁴³

a) \(\frac{2}{3}=\frac{8}{12}\) ; \(\frac{1}{4}=\frac{3}{12}\)

mà 8 > 3 ⇒ \(\frac{8}{12}>\frac{3}{12}\)⇒\(\frac{2}{3}>\frac{1}{4}\)

b) \(\frac{7}{10}\) và \(\frac{7}{8}\); mà 10 > 8 ⇒ \(\frac{7}{10}< \frac{7}{8}\)

c) \(\frac{6}{7}=\frac{30}{35}\); \(\frac{3}{5}=\frac{21}{35}\)

mà 30 > 21 ⇒ \(\frac{30}{35}>\frac{21}{35}\)⇒\(\frac{6}{7}>\frac{3}{5}\)

d) \(\frac{14}{21}=\frac{2}{3}\); \(\frac{60}{72}=\frac{5}{6}\)

\(\frac{2}{3}=\frac{4}{6}\) ⇒ \(\frac{2}{3}< \frac{5}{6}\)⇒ \(\frac{14}{21}< \frac{60}{72}\)

e) \(\frac{38}{133}=\frac{2}{7}\); \(\frac{129}{344}=\frac{3}{8}\)

\(\frac{2}{7}=\frac{16}{56}\) ; \(\frac{3}{8}=\frac{21}{56}\) mà 16<21 ⇒ \(\frac{16}{56}< \frac{21}{56}\)⇒ \(\frac{38}{133}< \frac{129}{344}\)

f) \(\frac{11}{54}=\frac{22}{108}\)và \(\frac{22}{37}\) mà 108 > 37 ⇒ \(\frac{22}{108}< \frac{22}{37}\)⇒ \(\frac{11}{54}< \frac{22}{37}\)

g) A > B

1) ta có:\(2^{150}\)= (2^3)^50=8^50

\(3^{100}\)= (3^2)^50 = 9^50

vì 8^50 < 9^50 => \(2^{150}\)<\(3^{100}\)

2^50=8^50

3^100=9^59

8^50<9^50

=>Đpcm

câu trả lời là ; <

giải chi tiết giúp tớ đi

1717/8585 = 17/85 = 1/5.  1313/5151=13/51.   Mà 1/5 <13/51

Vay 1718 <1313/5151

\(\frac{17}{85}vs\frac{13}{51}=\frac{1}{5}vs\frac{1}{3}\)

ta thấy 5>3

=>\(\frac{1717}{8585}< \frac{1313}{5151}\)

(-1/5)^9<(-1/25)^5

Ta có : 25^5 = (5^2)^5 = 5^10 < 5^9

=> -1/5^9 > -1/5^10

Hay -1/5^9 > 1/25^5