a,

Ta có:

16¹⁹ = (2⁴)¹⁹ = 2⁷⁶

8²⁵ = (2³)²⁵ = 2⁷⁵

Vì 2⁷⁶ > 2⁷⁵

Nên 16¹⁹ > 8²⁵.

b,

Ta có :

3^{10 =} 3^{2 .5} = (3²)⁵ = 9⁵

2¹⁵ - 2^{3 .5} = (2³)⁵ = 85
Vì 9^{5 >} 8⁵
Nên 3²⁰ > 2¹⁵

a,Ta có : \(16^{19}=\left(2^4\right)^{19}=2^{4.19}=2^{76}\)

\(8^{25}=\left(2^3\right)^{25}=2^{3.25}=2^{75}\)

Vì : \(2^{76}>2^{75}\Rightarrow16^{19}>8^{25}\)

b, Hình như đề sai bạn ạ .

c,Ta có : \(27^{11}=\left(3^3\right)^{11}=3^{3.11}=3^{33}\)

\(81^8=\left(3^4\right)^8=3^{4.8}=3^{32}\)

Vì : \(3^{33}>3^{32}\Rightarrow27^{11}>81^8\)

d, Ta có : \(625^5=\left(5^4\right)^5=5^{4.5}=5^{20}\)

\(125^7=\left(5^3\right)^7=5^{3.7}=5^{21}\)

Vì : \(5^{20}< 5^{21}\Rightarrow625^5< 125^7\)

e, Ta có : \(5^{36}=5^{3.12}=\left(5^3\right)^{12}=125^{12}\)

\(11^{24}=11^{2.12}=\left(11^2\right)^{12}=121^{12}\)

Vì : \(125^{12}>121^{12}\Rightarrow5^{36}>11^{24}\)

16¹⁹ và 8²⁵

ta có:

16¹⁹=(2⁴)¹⁹=2⁷⁶

8²⁵=(2³)²⁵=2⁷⁵

Vì 2⁷⁶> 2⁷⁵ => 16¹⁹>8²⁵

     27¹¹ và 81⁸

Ta có:

27¹¹=(3³)¹¹=3³³

81⁸=(3⁴)⁸=3³²

Vì 3³³>3³² => 27¹¹>81⁸

      625⁵ và 125⁷

ta có: 

625⁵=(5⁴)⁵=5²⁰

125⁷=(5³)⁷=5²¹

vì 5²⁰<5²¹

=>625⁵<125⁷

            5³⁶ và 11²⁴

Ta có:

5³⁶=(5³)¹²=125¹²

11²⁴=(11²)¹²=121¹²

Vì 125¹²>121¹² 

=>5³⁶>11²⁴

mai mình thi rồi, các bạn giúp mình với

Chờ tí

Câu 4: 

d) Ta có: \(\dfrac{-2}{17}+\dfrac{3}{19}+\dfrac{-15}{17}+\dfrac{16}{19}+\dfrac{5}{6}\)

\(=\left(-\dfrac{2}{17}-\dfrac{15}{17}\right)+\left(\dfrac{3}{19}+\dfrac{16}{19}\right)+\dfrac{5}{6}\)

\(=-1+1+\dfrac{5}{6}=\dfrac{5}{6}\)

Câu 3:

a) \(\dfrac{12}{36}=\dfrac{12:12}{36:12}=\dfrac{1}{3}\)

\(\dfrac{-16}{20}=\dfrac{-16:4}{20:4}=\dfrac{-4}{5}\)

b) \(\dfrac{21}{105}=\dfrac{21:21}{105:21}=\dfrac{1}{5}\)

\(\dfrac{35}{150}=\dfrac{35:5}{150:5}=\dfrac{7}{30}\)

Câu 4: 

a) \(\dfrac{3}{10}+\dfrac{5}{10}=\dfrac{3+5}{10}=\dfrac{8}{10}=\dfrac{4}{5}\)

b) Ta có: \(\left(-27\right)\cdot36+64\cdot\left(-27\right)+23\cdot\left(-100\right)\)

\(=\left(-27\right)\cdot\left(64+36\right)+23\cdot\left(-100\right)\)

\(=-27\cdot100-23\cdot100\)

\(=100\left(-27-23\right)\)

\(=-50\cdot100=-5000\)

c) \(\dfrac{5}{8}+\dfrac{3}{12}=\dfrac{15}{24}+\dfrac{6}{24}=\dfrac{21}{24}=\dfrac{7}{8}\)

d) Ta có: \(\dfrac{-2}{17}+\dfrac{3}{19}+\dfrac{-15}{17}+\dfrac{16}{19}+\dfrac{5}{6}\)

\(=\left(-\dfrac{2}{17}+\dfrac{-15}{17}\right)+\left(\dfrac{3}{19}+\dfrac{16}{19}\right)+\dfrac{5}{6}\)

\(=-1+1+\dfrac{5}{6}\)

\(=\dfrac{5}{6}\)

1. Từ bé đến lớn: \(\frac{3}{10};\frac{8}{15};\frac{9}{6};\frac{13}{5};\frac{16}{3}\)

2. 

a, Ta có: \(\frac{24}{36}=\frac{6}{9}\)  ;  \(\frac{15}{27}=\frac{5}{9}\)

Vì \(\frac{6}{9}>\frac{5}{9}\)nên \(\frac{24}{36}>\frac{15}{27}\)

P/s: Các câu còn lại tương tự :>