3⁵=3.3.3.3.3=243

5³=5.5.5=125

Vì: 243> 125=> 3⁵> 5³ (điều phải chứng minh)

3⁵=3.3.3.3.3=243

5³=5.5.5=125

Vì: 243> 125=> 3⁵> 5³ (điều phải chứng minh)

3⁵=3.3.3.3.3=243

5³=5.5.5=125

Vì: 243> 125=> 3⁵> 5³ (điều phải chứng minh)

a)300

biết làm nhưng trong lớp có ai tên vương bảo duy ko

Chi v?

\(a,4^{333}=\left(4^3\right)^{111}=64^{111}< 81^{111}=\left(3^4\right)^{111}=3^{444}< 3^{445}\\ b,39^{15}>36^{15}=\left(6^2\right)^{15}=6^{30}\\ c,25^{45}=\left(5^2\right)^{45}=5^{90}< 5^{102}=\left(5^3\right)^{34}=125^{34}\)

ta thấy: 5^300=5^3.100=(5^3)^100=125^100

            3^453=3^5.143=(3^5)^143=125^143

    Vì 100<143=>125^100<125^143

hay 5^300<3^453

vậy 5^300<3^453

Đề sai rồi

sao tính được

5^300 va 5^400 con giai dc . sai de rui bn

2⁹¹ = ( 2¹³ )⁷ = 8192⁷

5³⁵ = ( 5⁵ )⁷ = 3125⁷

Vì 8192 > 3125 => 2⁹¹ > 5³⁵

$2^{91}>2^{90}={32}^{18}$

         $5^{35}<5^{36}={25}^{18}$

        $\Rightarrow 2^{91}>{32}^{18}>{25}^{18}>5^{35}$

Vậy      $2^{91}>5^{35}$ 

$2^{91}>2^{90}={32}^{18}$

         $5^{35}<5^{36}={25}^{18}$

        $\Rightarrow 2^{91}>{32}^{18}>{25}^{18}>5^{35}$

Vậy      $2^{91}>5^{35}$ 

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

a, \(2^{15}=\left(2^3\right)^5=8^5\)

Vì \(8^5< 27^5\Rightarrow2^{15}< 27^5\)

b, \(4^8=\left(2^2\right)^8=2^{16}\)

\(8^6=\left(2^3\right)^6=2^{18}\)

Vì \(2^{16}< 2^{18}\Rightarrow4^8< 8^6\)

c, \(25^6=\left(5^2\right)^6=5^{12}\)

\(125^5=\left(5^3\right)^5=5^{15}\)

Vì \(5^{12}< 5^{15}\Rightarrow25^6< 125^5\)

hay- tích đi