a) 17^5 < 17^10

b) (98^4)^3 < 98^15

c) 2^60 > 4^20

<<<<< bé hơn

a) 16^30=(2^4)^30=2^120

32^15=(2^5)^15=2^75

Vậy, 16^30>32^15

b) 27^48=(3^3)^48=3^144

243^32=((3^5)^32=3^160

Vậy, 27^48<243^32.

Mình làm được 2 câu trên. Nhớ k cho mình.

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

b) \(64^7=\left(4^3\right)^7=4^{21}\)

Vậy \(4^{21}=64^7\)

a) 5²⁸ và 26¹⁴

   5²⁸ = (5²)¹⁴

    (5²)¹⁴ = 25¹⁴

    Vì 25¹⁴ < 26¹⁴ nên 5²⁸ < 26¹⁴ 

b) 4²¹ và 64⁷

    64⁷ = (4³)⁷ = 4²¹ = 4²¹

    Vậy 4²¹ = 64⁷ 

c) 31¹¹ và 17¹⁴

    31¹¹ < 32¹¹ = (2⁵)¹¹ = 2⁵⁵ 

    17¹⁴ > 16¹⁴ = (2⁴)¹⁴ = 2⁵⁶

    Vì 31¹¹ < 2⁵⁵ < 2⁵⁶ < 17¹⁴  nên 31¹¹ < 17¹⁴

d) 3²¹ và 2³¹

   3²¹ = 3x3²⁰ = 3x(3²)¹⁰ = 3x9¹⁰

    2³¹ = 2x2³⁰ = 2x(2³)¹⁰ = 2x8¹⁰

    3x9¹⁰ = 3x10x8¹⁰ = 30x8¹⁰

    => 3²¹ > 2³¹

   e) 3²ⁿ và 2³ⁿ

      3²ⁿ = (3²)ⁿ = 9ⁿ

      2³ⁿ = (2³)ⁿ = 8ⁿ 

      => 3²ⁿ > 2³ⁿ

a là <

b là >

Ta có : \(\frac{24}{56}< \frac{43}{56}\)

Vì 24 < 43

Ta có: \(\dfrac{10^{50}-3}{10^{50}+1}\)<\(\dfrac{10^{50}+1}{10^{50}+1}\)<\(\dfrac{10^{50}+1}{10^{50}-3}\)

=>\(\dfrac{10^{50}-3}{10^{50}+1}\)<​\(\dfrac{10^{50}+1}{10^{50}-3}\)​

vậy (đpcm)