\(\text{a, }2^{30}=8^{10}\)

     \(\text{ }3^{20}=\left(3^2\right)^{10}=9^{10}\)

\(\text{Vậy }2^{30}< 3^{20}\)

\(\text{b, }5^{300}=\left(5^3\right)^{100}=125^{100}\)

     \(3^{500}=\left(3^5\right)^{100}=243^{100}\)

\(\text{Vậy }5^{300}< 243^{100}\)

a, 2²²⁵ = 2^15.15= ( 2¹⁵)¹⁵ = 32768¹⁵

3¹⁵⁰ = 3^10.15 = ( 3¹⁰)¹⁵ = 59049¹⁵

Dễ thấy 32768 < 59049 nên 2²²⁵ < 3¹⁵⁰

hi

ỦA SAO BẠN GIẢI RA LUÔN RỒI. HAY Zậy?

đúng là hay quá ha.

tại mình ấn nhầm

a) Ta có \(\hept{\begin{cases}2^{24}=\left(2^6\right)^4=64^4\\3^{16}=\left(3^4\right)^4=81^4\end{cases}}\)

Mà \(64< 81\)

\(\Rightarrow64^4< 81^4\)

\(\Rightarrow2^{24}< 3^{16}\)

b) Ta có \(\hept{\begin{cases}2^{300}=\left(2^3\right)^{100}=8^{100}\\3^{200}=\left(3^2\right)^{100}=9^{100}\end{cases}}\)

Mà 8 < 9  

\(\Rightarrow8^{100}< 9^{100}\)

\(\Rightarrow2^{300}< 3^{200}\)

c) Ta có \(7^{20}=\left(7^4\right)^5=2401^5\)

Ta có 71 < 2401 

\(\Rightarrow71^5< 2401^5\)

\(\Rightarrow71^5< 7^{20}\)

!! K chắc câu c

@@ Học tốt

Chiyuki Fujito

a) \(2^{24}=\left(2^3\right)^8=8^8\)

\(3^{16}=\left(3^2\right)^8=9^8\)

Ta thấy 8<9\(\Rightarrow8^8< 9^8\Rightarrow2^{24}< 3^{16}\)

b) \(2^{300}=\left(2^3\right)^{100}=8^{100}\)

\(3^{200}=\left(3^2\right)^{100}=9^{100}\)

Thấy \(8< 9\Rightarrow8^{100}< 9^{100}\Rightarrow2^{300}< 3^{200}\)

c) \(7^{20}=\left(7^4\right)^5=2401^5\)

Ta thấy \(71< 2401\Rightarrow71^5< 2401^5\Rightarrow71^5< 7^{20}\)

1) \(99^{20}=\left(99^2\right)^{10}=9801^{10}< 9999^{10}\)

2) \(3^{21}=3^{20}\cdot3=9^{10}\cdot3\)

\(2^{31}=2^{30}\cdot2=8^{10}\cdot2\)

mà \(9^{10}\cdot3>8^{10}\cdot2\)=> tự viết tiếp

3) đợi chút

4³⁰ = (4³)¹⁰ = 64¹⁰ > 48¹⁰ = ( 2 . 24 )¹⁰ = ( 2¹⁰ ) . ( 24¹⁰ ) > 3 . 24¹⁰
 => 2³⁰ + 3³⁰ + 4³⁰ > 3 . 24¹⁰

.

a, 2²²⁵ = (2³)⁷⁵ = 8⁷⁵

3¹⁵⁰ = (3²)⁷⁵ = 9⁷⁵

Vì 8⁷⁵ < 9⁷⁵ nên 2²²⁵ < 3¹⁵⁰

b, 3³⁴ > 3³⁰ = (3³)¹⁰ = 27¹⁰

5²¹ > 5²⁰ = (5²)¹⁰ = 25¹⁰

Vì 27¹⁰ > 25¹⁰ => 3³⁰ > 5²⁰ => 3³⁴ > 5²¹

c, 3²¹ > 3²⁰ = (3²)¹⁰ = 9¹⁰

2³¹ > 2³⁰ = (2³)¹⁰ = 8¹⁰

Vì 9¹⁰ > 8¹⁰ => 3²¹ > 2³¹

d, 2⁹¹ > 2⁹⁰ = (2⁵)¹⁸ = 32¹⁸

5³⁵ < 5³⁶ = (5²)¹⁸ = 25¹⁸

Vì 32¹⁸ > 25¹⁸ => 2⁹¹ > 5³⁵

e, 99²⁰ = (99²)¹⁰ = 9801¹⁰ < 9999¹⁰

f, 12⁸.9¹² = 3⁸.4⁸.3²⁴ = 3³².2¹²

18¹⁶ = 2¹⁶.9¹⁶ = 2¹⁶.3³²

Vì 3³² . 2¹² < 2¹⁶.3³² => 12⁸.9¹² < 18¹⁶

g, 75²⁰ = 25²⁰.3²⁰ = 5⁴⁰.3²⁰

45¹⁰.5³⁰ = 5¹⁰.9¹⁰.5³⁰ = 5⁴⁰.3²⁰

Vậy 75²⁰ = 45¹⁰.5³⁰

what ?

a.\(2^{225}=\left(2^3\right)^{75}=8^{75}\left(1\right)\)

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

\(\left(1\right),\left(2\right)\Rightarrow2^{225}< 3^{150}\)

b.\(2^{91}=2^{7.13}=\left(2^{13}\right)^7=8192^7\left(1\right)\)

\(5^{35}=5^{7.5}=\left(5^5\right)^7=3125^7\left(2\right)\)

\(\left(1\right),\left(2\right)\Rightarrow5^{35}< 2^{91}\)

c.\(9999^{10}=\left(99.101\right)^{10}=99^{10}.101^{10}>99^{10}.99^{10}=99^{20}\)

\(\Rightarrow9999^{10}>99^{20}\)

Bài 2:

\(b.\)\(75^{20}=\left(3.5^2\right)^{20}=\left(3^{20}.5^{10}\right).5^{30}=\left[̣\left(3^2\right)^{10}.5^{10}\right].5^{30}=45^{10}.5^{30}\)

\(\Rightarrowđpcm\)

Bài 3:

a,\(25^4.2^8=\left(5^2\right)^4.2^8=5^8.2^8=10^8\)

b. \(\frac{27^2}{25^3}=\frac{\left(3^3\right)^2}{\left(5^2\right)^3}=\frac{3^6}{5^6}=\left(\frac{3}{5}\right)^3\)\(:v\)

\(27^2.25^3=3^6.5^6=15^6\)( đề phòng you viết sai đề )

a, Ta có : \(2^{333}=\left(2^3\right)^{111}=8^{111}\)

         \(3^{222}=\left(3^2\right)^{111}=9^{111}\)

Vì \(8^{111}< 9^{111}\Rightarrow2^{333}< 3^{222}\)

b, Ta có : \(9^{1005}=\left(3^2\right)^{1005}=3^{2010}\)

\(\Rightarrow3^{2009}< 9^{1005}\)

c, Ta có : \(99^{20}=\left(99^2\right)^{10}=9801^{10}\)

Vì \(9801^{10}< 9999^{10}\Rightarrow99^{20}< 9999^{10}\)

a) Ta có: \(2^{333}=\left(2^3\right)^{111}=8^{111}\)

\(3^{222}=\left(3^2\right)^{111}=9^{111}\)

Vì 9>8 nên 9¹¹¹>8¹¹¹

Vậy 3²²²>2³³³

b) Ta có: \(9^{1005}=\left(3^2\right)^{1005}=3^{2010}\)

Vì 2010>2009 nên 3²⁰¹⁰>3²⁰⁰⁹

Vậy 9¹⁰⁰⁵>3²⁰⁰⁹

c)Ta có:\(99^{20}=\left(99^2\right)^{10}=\left(99.99\right)^{10}\)

\(9999^{10}=\left(99.101\right)^{10}\)

Vì 99<101 nên (99.99)¹⁰<(99.101)¹⁰

Vậy 99²⁰<9999¹⁰