`@` `\text {Ans}`

`\downarrow`

\(202^{303}\text{ và }303^{202}\)

Ta có:

\(202^{303}=202^{3\cdot101}=\left(202^3\right)^{101}\)

\(303^{202}=303^{101\cdot2}=\left(303^2\right)^{101}\)

So sánh `202^3` và `303^2`, ta có:

`202^3 = (2*101)^3 = 2^3 * 101^3 = 8 * 101^3 = 8* 101^2 * 101 = 808*101^2`

`303^2 = (3*101)^2 = 3^2 * 101^2 = 9 * 101^2`

Vì `9 < 808 \Rightarrow 9*101^2 < 808*101^2`

`\Rightarrow`\(202^{303}>303^{202}\)

Vậy, \(202^{303}>303^{202}.\)

1+1=3

202³⁰³ = (202³)¹⁰¹ = 8242408¹⁰¹ > 91809¹⁰¹ = (303²)¹⁰¹ =303²⁰²

\(\text{#040911}\)

\(a,\)

\(202^{303}\text{ và }303^{202}\)

Ta có:

\(202^{303}=\left(202^3\right)^{101}=\left(101^3\cdot2^3\right)^{101}=\left(101^3\cdot8\right)^{101}\)

\(303^{202}=\left(303^2\right)^{101}=\left(101^2\cdot3^2\right)^{101}=\left(101^2\cdot9\right)^{101}\)

Ta có:

\(8\cdot101^3=8\cdot101\cdot101^2=808\cdot101^2\)

Vì \(808>9\)

\(\Rightarrow808\cdot101^2>9\cdot101^2\)

\(\Rightarrow202^{303}>303^{202}\)

\(b,\)

Ta có:

\(11^{1979}< 11^{1980}=\left(11^3\right)^{660}=1331^{660}\\ 37^{1320}=\left(37^2\right)^{660}=1369^{660}\\ \text{Vì }1331< 1369\\ \Rightarrow1331^{660}< 1369^{660}\\ \Rightarrow11^{1979}< 37^{1320}\)

mình cần gấp, giúp mình với 

a) \(202^{303}=\left(202^3\right)^{101}=8242408^{101}\)

\(303^{202}=\left(303^2\right)^{101}=91809^{101}< 8242408^{101}\)

\(202^{303}>303^{202}\)

Ta co : 202³⁰³ va 303²⁰²

=> 202³⁰³=(202²)¹⁰¹=40804¹⁰¹                     (1)

=>303²⁰²=(303³)¹⁰¹=27818127¹⁰¹             (2)

Tu (1) va (2) suy ra 202³⁰³<303²⁰²

lik e nhe

202³⁰³ = ( 2.101 )^3.101 = ( 2³.101³)¹⁰¹ = (8.101³)¹⁰¹

303²⁰² = (3.101)^2.101 = (3².101²)¹⁰¹ = (9.101²)¹⁰¹

Ta có : 8.101³ = 8.101.101² > 9.101²

=> 202³⁰³ > 303²⁰²

202³⁰³=202^3x101=(202³)¹⁰¹=8242408¹⁰¹

303²⁰²=303^2x101=(303²)¹⁰¹=91809¹⁰¹

  Vì 8242408¹⁰¹ > 91809¹⁰¹

        => 202³⁰³ > 91809¹⁰¹

Ta có:

\(202^{303}=\left(101.2\right)^{303}=101^{606}\)

\(303^{202}=\left(101.3\right)^{202}=101^{606}\)

Vì \(101^{606}=101^{606}\)nên \(202^{303}=303^{202}\)

Vậy \(202^{303}=303^{202}\)

mình nhầm => 202³⁰³ > 303²⁰²

Ta có : 303^202 = ( 303^2)^101 = 91809^101

202^303 = ( 202^3)^101 = 8242408^101

Vì 8242408^101 > 91809^101

Nên 303^202 < 202^303

Ta có :

303²⁰² = 101²⁰² . 3²⁰² = 101²⁰² . (3²)¹⁰¹ = 101²⁰² . 9¹⁰¹

202³⁰³ = 101³⁰³ . 2³⁰³ = 101³⁰³ . (2³)¹⁰¹ = 101³⁰³ .  8¹⁰¹

Vì 101²⁰² < 101³⁰³ ; 9¹⁰¹ > 8¹⁰¹

=> không so sánh được

Ta có :

\(303^{202}=\left(3.101\right)^{2.101}=\left(3^2.101^2\right)^{101}=\left(9.101^2\right)^{101}\)

\(202^{303}=\left(2.101\right)^{3.101}=\left(2^3.101^3\right)^{101}=\left(8.101.101^2\right)^{101}=\left(808.101^2\right)^{101}\)Vì 9 < 808 nên 303²⁰² < 202³⁰³

\(202^{303}=\left(202^3\right)^{101}=\text{8,242,408}^{101}\)

\(303^{202}=\left(303^2\right)^{101}=\text{91,809}^{101}\)

Vì : \(\text{8,242,408}^{101}>91809^{101}\)

Nên :\(202^{303}>303^{202}\)

202³⁰³ = ( 202³ )¹⁰¹ = 8242408¹⁰¹

303²⁰² = ( 303² )¹⁰¹ = 91809¹⁰¹

Vì 8242408 > 91809

=> 8242408¹⁰¹ > 91809¹⁰¹

=> 202³⁰³ > 303²⁰²

202³⁰³ = ( 202³ )¹⁰¹ = 8242408¹⁰¹

303²⁰² = ( 303² )¹⁰¹ = 91809¹⁰¹

Vì 8242408 > 91809

=> 8242408¹⁰¹ > 91809¹⁰¹

=> 202³⁰³ > 303²⁰²

Ta có : 202³⁰³ = (202³)¹⁰¹ = 8242408¹⁰¹

            303²⁰² = (303²)¹⁰¹ = 91809¹⁰¹

Vì 8242408¹⁰¹ > 91809¹⁰¹ => 202³⁰³ > 303²⁰²