a) Vì \(-45< -16\) nên \(\left(-\dfrac{45}{17}\right)^{15}< \left(\dfrac{-16}{17}\right)^{15}\)

b) Vì \(21< 23\) nên \(\left(-\dfrac{8}{9}\right)^{21}< \left(-\dfrac{8}{9}\right)^{23}\)

c) \(27^{40}=3^{3^{40}}=3^{120}\)

\(64^{60}=8^{2^{60}}=8^{120}\)

Vì \(3< 8\) nên \(3^{120}< 8^{120}\) hay \(27^{40}< 64^{60}\)

con ai kooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

co don quaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

a) ta có: 7^10 < 7^14 = (7^2)^7 = 49^7 < 50^7

=> 7^10 < 50^7

b) ta có: 5^30 = (5^3)^10 = 125^10 > 124^10

=> 5^30 > 124^10

c) ta có: 9^21 = (9^3)^7=729^7

phần d thì mk ko bk, xl bn nha

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b,>

c,=

^_^

a) Ta có :

\(27^{27}>27^{26}=\left(27^2\right)^{13}=729^{13}>243^{13}\)

\(\Rightarrow27^{27}>243^{13}\)

\(\Rightarrow-27^{27}< -243^{13}\)

\(\Rightarrow\left(-27\right)^{27}< \left(-243\right)^{13}\)

b) \(\left(\dfrac{1}{8}\right)^{25}>\left(\dfrac{1}{8}\right)^{26}=\left(\dfrac{1}{8^2}\right)^{13}=\left(\dfrac{1}{64}\right)^{13}>\left(\dfrac{1}{128}\right)^{13}\)

\(\Rightarrow\left(\dfrac{1}{8}\right)^{25}>\left(\dfrac{1}{128}\right)^{13}\)

\(\Rightarrow\left(-\dfrac{1}{8}\right)^{25}< \left(-\dfrac{1}{128}\right)^{13}\)

c) \(4^{50}=\left(4^5\right)^{10}=1024^{10}\)

\(8^{30}=\left(8^3\right)^{10}=512^{10}< 1024^{10}\)

\(\Rightarrow4^{50}>8^{30}\)

d) \(\left(\dfrac{1}{9}\right)^{17}< \left(\dfrac{1}{9}\right)^{12}< \left(\dfrac{1}{27}\right)^{12}\)

\(\Rightarrow\left(\dfrac{1}{9}\right)^{17}< \left(\dfrac{1}{27}\right)^{12}\)

a) Ta có :

2727>2726=(272)13=72913>243132727>2726=(272)13=72913>24313

⇒2727>24313⇒2727>24313

⇒−2727<−24313⇒−2727<−24313

⇒(−27)27<(−243)13⇒(−27)27<(−243)13

b) (18)25>(18)26=(182)13=(164)13>(1128)13(81​)25>(81​)26=(821​)13=(641​)13>(1281​)13

⇒(18)25>(1128)13⇒(81​)25>(1281​)13

⇒(−18)25<(−1128)13⇒(−81​)25<(−1281​)13

c) 450=(45)10=102410450=(45)10=102410

830=(83)10=51210<102410830=(83)10=51210<102410

⇒450>830⇒450>830

d) (19)17<(19)12<(127)12(91​)17<(91​)12<(271​)12

⇒(19)17<(127)12⇒(91​)17<(271​)12

nhanh lên các bn m còn 30 p nữa sắp phải nộp rùi

ai trả lời nhanh nhất m k cho

hay- tích đi

a) ta có: 3¹⁰⁰ = (3²)⁵⁰ = 9⁵⁰

b) ta có: 3³⁰ = (3³)¹⁰ = 27¹⁰ > 8¹⁰

c) ta có: 36.6⁷ = 6².6⁷ = 6⁹ 

Lại có: 4³³ > 4²⁷ = (4³)⁹ = 64⁹ > 6⁹

=> 4³³>36.6⁷

\(a,\)\(3^{100}\)\(=3^{2.50}\)=\(\left(3^2\right)\)\(^{50}\)\(=9^{50}\)

\(\Rightarrow\)\(3^{100}\)= \(9^{50}\)

b,\(3^{30}\)\(=3^{3.10}\)\(=\left(3^3\right)\)\(^{10}\)\(=27^{10}\)

\(\Rightarrow\)\(3^{30}\)\(>8^{10}\)

31¹¹<32¹¹=2⁵⁵

17¹⁴>16¹⁴=2⁵⁶

=>Vì 2⁵⁵<2⁵⁶ nên 31¹¹<17¹⁴.

a) 5¹⁴ = 5^2.7= (5²)⁷= 25⁷

3²¹= 3^3.7= (3³)⁷= 27⁷

Mà 25 < 27 

=> 5¹⁴<3²¹

b) 4³³= (4³)¹¹  = 64¹¹

3⁴⁴= (3⁴)¹¹ = 81¹¹

=> 4³³<3⁴⁴

c) 2¹⁶¹ > 2¹⁶⁰ = (2⁴)⁴⁰= 16⁴⁰

Mà 13⁴⁰< 16⁴⁰ < 2¹⁶¹

=> 13⁴⁰<2¹⁶¹

d) 17¹⁵= 17^3.5= (17³)⁵ = 4913⁵

31¹⁰= (31²)⁵= 961⁵

Mà 4913 > 961

=> 17¹⁵> 31¹⁰

e) 2²⁵⁵ = (2⁵)⁴⁵ = 32⁴⁵

3¹⁸⁰ = (3⁴)⁴⁵ = 81⁴⁵

=> 2²⁵⁵ < 3¹⁸⁰

g) 202³⁰³ = (202³)¹⁰¹ = (101³.2³)¹⁰¹= (101³.8)¹⁰¹= (101².8.101)¹⁰¹= (101².808)¹⁰¹

303²⁰² = (303²)¹⁰¹= (3².101²)¹⁰¹= (101².9) ¹⁰¹

Vì 101².9 < 101².808

=> 202³⁰³>303²⁰²

a,3²⁰ và 27⁴

3²⁰=(3⁵)⁴=243⁴>27⁴

Vậy 3²⁰>27⁴

b,5³⁴ và 25x5³⁰

25x5³⁰=5²x5³⁰=5³²<5³⁴

=>5³⁴>25x5³⁰.

c,2²⁴và 26⁶

2²⁴=(2⁴)⁶=16⁶<26⁶

=>2²⁴<26⁶

d,10³⁰và 4⁵⁰

10³⁰=(10³)¹⁰=1000¹⁰

4⁵⁰=(4⁵)¹⁰=1024¹⁰

Vì 1000¹⁰<1024¹⁰nên 10³⁰<4⁵⁰.

e,2³⁰⁰và 3²⁰⁰

2³⁰⁰=(2³)¹⁰⁰=8¹⁰⁰

3²⁰⁰=(3²)¹⁰⁰=9¹⁰⁰

Vì 8¹⁰⁰<9¹⁰⁰ nên 2³⁰⁰<3²⁰⁰