Trả lời :

19.90 < 31.60

=> m < n

~HT~

m = 19.90 = 19. 3.30 =57.30

n = 31.60 = 31.2.30 = 64.30

m < n

a, m = 19.90 = 19.3.30 = 57.30

    n = 31.60 = 31.2.30 = 62.30

    n > m

b, 2011 < 2015

    2012 < 2015

  2011.2012 < 2015.2015

   p < q

a)m<n

b)p<q

Ta có: 19/31 < 19/30 < 20/30 (Mà: 20/30 = 60/90)

Vậy: 19 x 90 < 31 x 60

Vậy: A < B

A = 19 × 90 = 19 × 3 × 30 = 57 × 30

B = 31 × 60 = 31 × 2 × 30 = 62 × 30

Do 57 < 62 nên 57 × 30 < 62 × 30

⇒ 19 × 90 < 31 × 60

Vậy A < B

A = 19 . 90 = ( 20 - 1 ) . 90 = 1800 - 90 < 1800

B = 31 . 60 = ( 30 + 1 ) . 60 = 1800 + 60 > 1800

Vì A < 1800 < B

=> A < B

Ta có : C = 2021 . 2019  mà D = 2015 . 2015

Vì 2021 > 2015 và 2019 > 2015 => 2021 . 2019 > 2015 . 2015 

=> C > D

Ta có : 

A = 19 . 90 = 19 . 3 . 30 = 57 . 30

B = 31 . 60 = 31 . 2 . 30 = 62 . 30

Vì 57 < 62 hơn 57 . 30 < 62 . 30 hay 19 . 90 < 31 . 60

=>A=123 .  135 . 1000+135

=>B= 135.123 . 1000+123

 Vì 135> 123

=>A>B

Vậy A>B

A < B

a: \(6\sqrt{3}=\sqrt{108}>\sqrt{54}=3\sqrt{6}\)

\(\Rightarrow5^{6\sqrt{3}}>5^{3\sqrt{6}}\)

b: \(\sqrt{2}\cdot2^{\dfrac{2}{3}}=2^{\dfrac{1}{2}}\cdot2^{\dfrac{2}{3}}=2^{\dfrac{1}{2}+\dfrac{2}{3}}=2^{\dfrac{7}{6}}\)

\(\left(\dfrac{1}{2}\right)^{-\dfrac{4}{3}}=2^{\left(-1\right)\cdot\left(-\dfrac{4}{3}\right)}=2^{\dfrac{4}{3}}\)

mà \(\dfrac{7}{6}< \dfrac{8}{6}=\dfrac{4}{3}\).

nên \(\sqrt{2}\cdot2^{\dfrac{2}{3}}< \left(\dfrac{1}{2}\right)^{-\dfrac{4}{3}}\).