a) \(10^{30}=2^{30}.5^{30}=2^{30}.\left(5^3\right)^{10}=2^{30}.125^{10}\)

\(2^{100}=2^{30}.2^{70}=2^{30}.\left(2^7\right)^{10}=2^{30}.128^{10}\)

mà \(125^{10}< 128^{10}\)

\(\Rightarrow10^{30}< 2^{100}\)

b) \(5^{40}=\left(5^4\right)^{10}=625^{10}>620^{10}\)

\(5^{40}>620^{10}\)

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

\(16^{19}=\left(2^4\right)^{19}=2^{76}>2^{75}\)

\(\Rightarrow16^{19}>8^{25}\)

a,10³⁰ và 2¹⁰⁰

10³⁰=(10³)¹⁰=1000¹⁰

2¹⁰⁰=(2¹⁰)¹⁰=1024¹⁰

Vì 1000¹⁰<1024¹⁰ nên 10³⁰<2¹⁰⁰.

b,5⁴⁰ và 620¹⁰

5⁴⁰=(5⁴)¹⁰=625¹⁰>620¹⁰

=>5⁴⁰>620¹⁰.

c,8²⁵ và 16¹⁹

Nhân 8²⁵ và 16¹⁹ với 4 , ta được 

32²⁵ và 64¹⁹

32²⁵=(32⁵)⁵=33554432⁵

64¹⁹<64²⁰=(64⁴)⁵=16777216⁵

Vì 33554432⁵>16777216⁵ nên 8²⁵>16¹⁹

\(A=-\frac{9}{10^{2010}}-\frac{19}{10^{2011}}=-\frac{9}{10^{2010}}-\frac{9}{10^{2011}}-\frac{10}{10^{2011}}=-\frac{9}{10^{2010}}-\frac{9}{10^{2011}}-\frac{1}{10^{2010}}=\frac{8}{10^{2010}}-\frac{9}{10^{2011}}\)\(>B=-\frac{19}{10^{2010}}-\frac{9}{10^{2011}}\)

a,>

b,>

c,<

a, 19²⁰ > 9⁸

b, 5⁴⁰ < 620¹⁰

c, Ta có: \(2^{161}=2^{7.23}=\left(2^7\right)^{23}=128^{23}\)

=> 128²³ > 13⁴⁰ hay 2¹⁶¹ > 13⁴⁰

a) ta thấy :

cơ số : \(19>9\)

mũ số : \(20>8\)

\(\Rightarrow19^{20}>9^8\)

b) \(5^{40}v\text{à}620^{10}\)

ta có \(5^{40}=\left(5^4\right)^{10}=625^{10}\)

ta thấy 

cơ số : \(625>620\)

mũ số : \(10=10\)

\(\Rightarrow625^{10}>620^{10}\)

\(\Rightarrow5^{40}>620^{10}\)

3^19 > 11^10

\(3^{19}< 3^{20}=\left(3^2\right)^{10}=9^{10}< 11^{10}\)