a) \(15^{40}=\left(15^4\right)^{10}=50625^{10}>5832^{10}=\left(18^3\right)^{10}=18^{30}\)

b)\(180^{300}=\left(180^3\right)^{100}=5832000^{100}>2015^{100}\)

1:

a: Vì \(\dfrac{-4}{3}=\dfrac{-4\cdot3}{3\cdot3}=\dfrac{-12}{9}=\dfrac{12}{9}\\ \Rightarrow\dfrac{-4}{3}=\dfrac{12}{9}\)

b: Vì : \(-2\cdot3=-6\\ -6\cdot8=-48\)

nên 2 p/s ko bằng nhau 

thật luôn

1) \(15^{40}=15^{4.10}=\left(15^4\right)^{10}=50625^{10}\)

    \(18^{30}=18^{3.10}=\left(18^3\right)^{10}=5832^{10}\)

Vì \(50625^{10}>5832^{10}\) Nên \(15^{40}>18^{30}\)

2)\(180^{300}=180^{3.100}=\left(18^3\right)^{100}=5832^{100}\)

Vì \(2015^{100}

A=1+2+2^2+2^3+....+2^9

2A=2+2^2+2^3+....+2^10

2A-A=2^10-1

A=2^10-1/2

B=5.2^8=(2^2+1).2^8=2^10+2^8

=>B>A

2A = 2(1 + 2 + 2² + .... + 2⁹ )

= 2 + 2² + 2³ + ..... + 2¹⁰

2A - A = (2 + 2² + 2³ + ..... + 2¹⁰) - (1 + 2 + 2² + .... + 2⁹ )

A = 2¹⁰ - 1  

B = 5.2⁸ = (2² + 1).2⁸ = 2¹⁰ + 2⁸

2¹⁰ - 1 < 2¹⁰ + 2⁸

=> A < B

a: \(17A=\dfrac{17^{19}+17}{17^{19}+1}=1+\dfrac{16}{17^{19}+1}\)

\(17B=\dfrac{17^{18}+17}{17^{18}+1}=1+\dfrac{16}{17^{18}+1}\)

mà 17^19+1>17^18+1

nên A<B

b: \(2C=\dfrac{2^{2021}-2}{2^{2021}-1}=1-\dfrac{1}{2^{2021}-1}\)

\(2D=\dfrac{2^{2022}-2}{2^{2022}-1}=1-\dfrac{1}{2^{2022}-1}\)

2^2021-1<2^2022-1

=>1/2^2021-1>1/2^2022-1

=>-1/2^2021-1<-1/2^2022-1

=>C<D

cho mình bài c với đc ko?mình ko bik làm😫😖

a) 16¹⁹ và 8²⁵ 

Ta có :

16¹⁹ = ( 2⁴ )¹⁹ = 2⁷⁶

8²⁵ = ( 2³ )²⁵ = 2⁷⁵

Vì 2⁷⁶ > 2⁷⁵ Nên 16¹⁹ > 8²⁵

b) 5³⁶ và 11²⁴

Ta có :

5³⁶ = ( 5³ )¹² = 125¹²

11²⁴ = ( 11² )¹² = 121¹²

Vì 125¹² > 121¹² Nên 5³⁶ > 11²⁴

1.

\(M=3^0+3^1+......+3^{50}.\)

\(\Rightarrow3M=3+3^2+.......+3^{51}\)

\(\Rightarrow3M-M=\left(3+3^2+.......+3^{51}\right)-\left(3^0+3+.....+3^{50}\right)\)

\(\Rightarrow2M=3^{51}-1\)

\(\Rightarrow M=\frac{3^{51}-1}{2}\)

2.

\(a,\)Ta có : \(16^{19}=\left(2^4\right)^{19}=2^{76}\)

                     \(8^{25}=\left(2^3\right)^5=2^{75}\)

Vì \(2^{76}>2^{75}\Rightarrow16^{19}>8^{25}\)

\(b,\)Ta có : \(5^{36}=\left(5^3\right)^{12}=125^{12}\)

                      \(11^{24}=\left(11^2\right)^{12}=121^{12}\)

Vì \(125^{12}>121^{12}\Rightarrow5^{36}>11^{24}\)

giúp mik với mn ơi

a: 1/3=8/24

b: 2/7=14/49<14/30

c: 15/35=3/7

d: 8/32=2/8

e: 10/20=100/200