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

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

Vì \(8^{100}< 9^{100}\) nên \(2^{300}< 3^{200}\)

\(b,8^5=32768\)

\(6^6=46656\)

Vì \(32768< 46656\) nên \(8^5< 6^6\)

\(c,3^{450}=\left(3^3\right)^{150}=27^{150}\)

\(5^{300}=\left(5^2\right)^{150}=25^{150}\)

Vì \(27^{150}>25^{150}\) nên \(3^{450}>5^{300}\)

#Ayumu

a, Ta có: \(\left(\dfrac{1}{2}\right)^{300}=\left[\left(\dfrac{1}{2}\right)^3\right]^{100}=\left(\dfrac{1}{8}\right)^{100}\)
\(\left(\dfrac{1}{3}\right)^{200}=\left[\left(\dfrac{1}{3}\right)^2\right]^{100}=\left(\dfrac{1}{9}\right)^{100}\)
=> \(\left(\dfrac{1}{8}\right)^{100}>\left(\dfrac{1}{9}\right)^{100}\)=> \(\left(\dfrac{1}{2}\right)^{300}>\left(\dfrac{1}{3}\right)^{200}\)
b, Ta có: \(\left(\dfrac{1}{3}\right)^{75}=\left[\left(\dfrac{1}{3}\right)^3\right]^{25}=\left(\dfrac{1}{27}\right)^{25}\)
\(\left(\dfrac{1}{5}\right)^{50}=\left[\left(\dfrac{1}{5}\right)^2\right]^{25}\)\(=\left(\dfrac{1}{25}\right)^{25}\)
Do \(\left(\dfrac{1}{27}\right)^{25}< \left(\dfrac{1}{25}\right)^{25}=>\left(\dfrac{1}{3}\right)^{75}< \left(\dfrac{1}{5}\right)^{50}\)
Kiểm tra lại bài nhé, học tốt!!

a: 99^20=9801^10<9999^10

b: 3^500=243^100

5^300=125^300

=>3^500>5^300

`a)2^{300}=(2^3)^100=8^100`

`3^200=(3^2)^100=9^100`

Vì `9^100>8^100`

`=>2^300<3^200`

`b)3xx24^10`

`=3.(3.8)^10`

`=3^{11}.8^10`

`=3^{11}.2^30`

`2^300=2^{30}.2^{270}`

`=2^{30}.8^{90}`

Vì `3^11<8^90`

`=>3^{11}.2^30<8^{90}.2^30=2^300`

`=>3xx24^{10}<2^300+3^20+4^30`

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

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

Thấy 8<9 => \(8^{100}< 9^{100}\)=> \(|-2|^{300}< |-3|^{200}\)

a) TA CÓ

|-2|³⁰⁰=2³⁰⁰=2^2*150=(2²)¹⁵⁰=4¹⁵⁰

mà |-4|¹⁵⁰=4¹⁵⁰

=>bằng nhau

b)TA CÓ

|-2|³⁰⁰=2³⁰⁰=2^3*100=(2³)¹⁰⁰=8¹⁰⁰

mà |-3|²⁰⁰=3²⁰⁰=3^2*100=(3²)¹⁰⁰=9¹⁰⁰

^{=>bé hơn}

a) Ta có : |-2|300  =  2 . 300 = 600            | -4|150 = 4 . 150 = 600

Vì 600 = 600 nên |-2|300  =  |-4|150

b) Ta có : |-2|300  =  2 . 300 = 600           |-3|200  =  3 . 200 = 600 

Vì 600  =  600  nên | -2| 300  =   | -3 |200

Bài 1:

a: Sửa đề: 1/3^200

1/2^300=(1/8)^100

1/3^200=(1/9)^100

mà 1/8>1/9

nên 1/2^300>1/3^200

b: 1/5^199>1/5^200=1/25^100

1/3^300=1/27^100

mà 25^100<27^100

nên 1/5^199>1/3^300

a, Chia hết cho 3 thì nhóm 2 số thành 1 cặp ; chia hết cho 7 thì nhóm 3 số thành 1 cặp

b, Đề phải là A = 2009.2011

Có :A = 2009.(2010+1) = 2009.2010+2009

= 2009.2010+2010-1 = 2010.(2009+1)-1 = 2010^2-1

Vì 2010^2-1 < 2010^2 = B => A < B

c, A = (3^3)^150 = 27^150

B = (5^2)^150 = 25^150

Vì 27^150 > 25^150 => A > B

k mk nha