1/2^1050 <   5^450

2/5^2n   < 2^2n

3/3^500  <  7^300

4/8^5 <   3.4^7

5/99^20 < 9999^10

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1 ) Ta có :

3²⁴⁶⁸⁰ = ( 3² )¹²³⁴⁰ = 9¹²³⁴⁰

2³⁷⁰²⁰ = ( 2³ )¹²³⁴⁰ = 8¹²³⁴⁰

Vì 9¹²³⁴⁰ > 8¹²³⁴⁰ nên 3²⁴⁶⁸⁰ > 2³⁷⁰²⁰

2 ) Ta có :

2¹⁰⁵⁰ = ( 2⁷ )¹⁵⁰ = 128¹⁵⁰

5⁴⁵⁰ = ( 5³ )¹⁵⁰ = 125¹⁵⁰

Vì 128¹⁵⁰ > 125¹⁵⁰ nên 2¹⁰⁵⁰ > 5⁴⁵⁰

\(2^{91}=\left(2^{13}\right)^7=73728^7\)

\(5^{35}=\left(5^5\right)^7=3125^7\) nhỏ hơn \(73728^7\)

\(\Rightarrow2^{91}\) lớn hơn \(5^{35}\)

\(b,3^{400}=\left(3^4\right)^{100}=81^{100}\\ 4^{300}=\left(4^3\right)^{100}=64^{100}\\ Vì:81^{100}>64^{100}\left(Do:81>64\right)\\ \Rightarrow3^{400}>4^{300}\)

\(d,10^{20}=\left(10^2\right)^{10}=100^{10}\\ Vì:100^{10}>20^{10}\left(Do:100>20\right)\\ \Rightarrow10^{20}>20^{10}\)

a, Ta có:

\(2^{225}=2^{3.75}=\left(2^3\right)^{75}=8^{75}\)

\(3^{150}=3^{2.75}=\left(3^2\right)^{75}=9^{75}\)

Vì \(8^{75}< 9^{75}\)nên \(2^{225}< 3^{150}\)

b, Ta có:

\(2^{91}=2^{13.7}=\left(2^{13}\right)^7=8192^7\)

\(5^{35}=5^{5.7}=\left(5^5\right)^7=3125^7\)

Vì \(8192^7>3125^7\)nên \(2^{91}>5^{35}\)

2^225>3^150

2^91<5^35

99^20<9999^10

a, 2²²⁵ và 3¹⁵⁰
2²²⁵ = ( 2³ )⁷⁵ = 8⁷⁵
3¹⁵⁰ = ( 3² )⁷⁵ = 9⁷⁵
Do 8⁷⁵ < 9⁷⁵ nên 2²²⁵ < 3¹⁵⁰ 
b,c tương tự
 

f: 11^1979<11^1980=1331^660

37^1320=(37^2)^660=1369^660

1331<1369

=>1331^660<1369^660

=>11^1980<37^1320

=>11^1979<37^1320

g: 10^10=2^10*5^10

48*50^5=2^4*3*2^5*5^10=2^9*3*5^10

2^10<2^9*3

=>2^10*5^10<2^9*3*5^10

=>10^10<48*50^5