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

a) | - 2 |³⁰⁰và | - 4 | ¹⁵⁰

^{\(\Rightarrow\)} | - 2 |³⁰⁰=2³⁰⁰

\(\Rightarrow\)| - 4 | ¹⁵⁰=4¹⁵⁰=(2²)¹⁵⁰=2³⁰⁰

^{\(\Rightarrow\)}2³⁰⁰=2³⁰⁰

^Vậy | - 2 |³⁰⁰=| - 4 | ¹⁵⁰

a) | - 2 |^{300 =} | - 4 | ¹⁵⁰

b) | - 2 | ³⁰⁰ < | - 3 | ²⁰⁰

a) \(\left|-2\right|^{300}=2^{300}=\left(2^2\right)^{150}=4^{150}\)

\(\left|-4\right|^{150}=4^{150}\)

vì \(4^{150}=4^{150}\)nên \(\left|-2\right|^{300}=\left|-4\right|^{150}\)

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

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

vì \(8^{100}< 9^{100}\)nên \(\left|-2\right|^{300}< \left|-3\right|^{200}\)

`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`

a)\(\left|-2\right|^{300}=2^{300}=\left(2^2\right)^{150}=4^{150}\) ; \(\left|-4\right|^{150}=4^{150}\)

\(\Rightarrow\left|-2\right|^{300}=\left| -4\right|^{150}\)

b) \(\left|-2\right|^{300}=2^{300}=\left(2^3\right)^{100}=8^{100}\) ; \(\left|-3\right|^{200}=3^{200}=\left(3^2\right)^{100}=9^{100}\)

Mà 8 < 9 \(\Rightarrow8^{100}< 9^{100}\) hay \(\left|-2\right|^{300}< \left|-3\right|^{200}\)

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,2³⁰⁰=4¹⁵⁰

b,2³⁰⁰<3²⁰⁰

a. \(\left|-2\right|^{300}=2^{300};\left|-4\right|^{150}=4^{150}=\left(2^2\right)^{150}=2^{300}\)

Mà \(2^{300}=2^{300}\)

Vậy \(\left|-2\right|^{300}=\left|-4\right|^{150}\).

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

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

Vì 8 < 9 nên 8¹⁰⁰ < 9¹⁰⁰

Vậy \(\left|-2\right|^{300}<\left|-3\right|^{200}\).

a)

= 2³⁰⁰  và  4¹⁵⁰

4¹⁵⁰ = (2²)¹⁵⁰ = 2³⁰⁰

vì 2³⁰⁰ = 2³⁰⁰

\(\Rightarrow\)|-2|³⁰⁰ = |-4|¹⁵⁰

b) = 2³⁰⁰ và 3²⁰⁰

2³⁰⁰ = (2³)¹⁰⁰ = 8¹⁰⁰ 

3²⁰⁰ = (3²)¹⁰⁰ = 9¹⁰⁰

vì 8¹⁰⁰ < 9¹⁰⁰

^=>  2³⁰⁰ < 3²⁰⁰

200³⁰⁰ = 200^3.100 = (200³)¹⁰⁰ = 8000000¹⁰⁰

300²⁰⁰ = 300^2.100 = (300²)¹⁰⁰ = 90000¹⁰⁰

Vì 8000000¹⁰⁰ > 90000¹⁰⁰

=> 200³⁰⁰ > 300²⁰⁰

200³⁰⁰=(200³)¹⁰⁰=8000000¹⁰⁰

300²⁰⁰=(300²)¹⁰⁰=90000¹⁰⁰

Vì 8000000>90000=>8000000¹⁰⁰>90000¹⁰⁰

=>200³⁰⁰>300²⁰⁰