Xét \(A=2^{30}+3^{30}+4^{30}=\left(2^3\right)^{10}+\left(3^3\right)^{10}+\left(2^2\right)^{30}=8^{10}+27^{10}+2^{60}\)

\(B=3^{20}+6^{20}+8^{20}=\left(3^2\right)^{10}+\left(6^2\right)^{10}+\left(2^3\right)^{20}=9^{10}+36^{10}+2^{60}\)

Vì \(8^{10}< 9^{10},27^{10}< 36^{10}\)nên A<B

2³⁰ = 2^3.10= 8¹⁰

3³⁰=3^3.10=27¹⁰

4³⁰=4^3.10=64¹⁰

Vế trái = 8¹⁰ + 27¹⁰ + 64¹⁰

3²⁰=3^2.10=9¹⁰

6²⁰=6^2.10=36¹⁰

8²⁰=8^2.10=64¹⁰

vế phải = 9¹⁰ + 36¹⁰ + 64¹⁰

Vì 64¹⁰=64¹⁰ ; 36¹⁰ > 27¹⁰ ; 9¹⁰ > 8¹⁰

=> vế phải > vế trái

so sánh: 2^30 + 3^30 + 4^30 và 3^20 + 6^20 + 8^20
2^30 = ( 2^3)^10 = 8^ 10
3^30 = (3^3)^10 = 27^10
4^30 = (4^3)^10 = 64^10
3^20 = (3^2)^10 = 9^10
6^20 = (6^2) = 36^10
8^20 = (8^2)^10 = 84^10
vì 9^10 > 8^10
36^10 > 27^10
84^10 > 64^10
=> 2^30 + 3^30 + 4^30 < 3^20 + 6^20 + 8^20

Ta có: \(2^{30}=2^{3.10}=\left(2^3\right)^{10}=8^{10}\)

            \(3^{20}=3^{2.10}=\left(3^2\right)^{10}=9^{10}\)

Vì 8 < 9 nên 8¹⁰ < 9¹⁰

Vậy 2³⁰ < 3²⁰

2^30=2^3.10=(2^3)^10  =  8^10

3^20=3^2.10=(3^2)^10=9^10

VÌ 9<8 NÊN 2^30<3^20

Thfkfifi

𝓓𝓪̣𝓷𝓰 𝓷𝓪̀𝔂 𝓵𝓪̀ 𝓭𝓪̣𝓷𝓰 𝓭𝓾̛𝓪 𝓿𝓮̂̀ 𝓬𝓾̀𝓷𝓰 𝓼𝓸̂́ 𝓶𝓾̃ 𝓭𝓮̂̉ 𝓼𝓸 𝓼𝓪́𝓷𝓱 𝓷𝓱𝓪 𝓫𝓷!𝓣𝓪 𝓬𝓸́ : \(2^{30}=\left(2^{10}\right)^{20}=1024^{20}\)

𝓥𝓲̀ : \(1024>3\) 𝓷𝓮̂𝓷 \(1024^{20}>3^{20}\)

\(\Rightarrow2^{30}>3^{20}\)

2³⁰ = (2³)¹⁰ = 8¹⁰

3²⁰ = (3²)¹⁰ = 9¹⁰

Ta thấy: 8<9

=> 8¹⁰ < 9¹⁰

vậy 2³⁰ < 3²⁰

2³⁰ = (2³)¹⁰ = 8¹⁰

3²⁰ = (3²)¹⁰ = 9¹⁰

Vì 8¹⁰ < 9¹⁰ nên 2³⁰ < 3²⁰

2^30 < 3^20

Ta có:

\(2^{30}=\left(2^3\right)^{10}=8^{10}\)

\(3^{20}=\left(3^2\right)^{10}=9^{10}\)

\(\Rightarrow8^{10}< 9^{10}\Rightarrow2^{30}< 3^{20}\)

ai k mik mik k lại

ta có \(2^{30}=\left(2^3\right)^{10}=8^{10}\)

        \(3^{30}=\left(3^3\right)^{10}=27^{10}\)

        \(4^{30}=\left(4^3\right)^{10}=64^{10}\)

   ta có       \(3^{20}=\left(3^2\right)^{10}=9^{10}\)

                  \(6^{20}=\left(6^2\right)^{10}=36^{10}\)

                   \(8^{20}=\left(8^2\right)^{10}=64^{10}\)

              \(\Rightarrow2^{30}+3^{30}+4^{30}=8^{10}+27^{10}+64^{10}\)

            \(\Rightarrow3^{20}+6^{20}+8^{20}=9^{10}+36^{10}+64^{10}\)

       Xét        \(8^{10}

So sánh 2^20+3^30+4^30 và3.24^10

`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`

\(2^{30}=\left[2^3\right]^{10}=8^{10}\)

\(3^{20}=\left[3^2\right]^{10}=9^{10}\)

Vì 8¹⁰ < 9¹⁰ nên 2³⁰ < 3²⁰

2³⁰ < 3²⁰

\(2^{30}=\left(2^3\right)^{10}=8^{10}\)

\(3^{20}=\left(3^2\right)^{10}=9^{10}\)

\(\Rightarrow8^{10}< 9^{10}\Rightarrow2^{30}< 3^{20}\)

Vậy \(2^{30}< 3^{20}\)

Ai thấy đúng hì nhấn vào chữ " đúng: hộ mik nha

Lời giải:

a.

$32^{47}=(2^5)^{47}=2^{5.47}=2^{235}$

$64^{33}=(2^6)^{33}=2^{6.33}=2^{198}$

Vì $2^{235}> 2^{198}$ nên $32^{47}> 64^{33}$

b.

$(\frac{1}{2})^{30}=\frac{1}{2^{30}}=\frac{1}{8^{10}}$

$(\frac{1}{3})^{20}=\frac{1}{3^{20}}=\frac{1}{9^{10}}$

Hiển nhiên $8^{10}< 9^{10}\Rightarrow \frac{1}{8^{10}}> \frac{1}{9^{10}}$

$\Rightarrow (\frac{1}{2})^{30}> (\frac{1}{3})^{20}$

Ta có: \(2^{30}+3^{30}+4^{30}=\left(2^3\right)^{10}+\left(3^3\right)^{10}+\left(4^3\right)^{10}=8^{10}+27^{10}+64^{10}\)

\(3^{20}+6^{20}+8^{20}=\left(3^2\right)^{10}+\left(6^2\right)^{10}+\left(8^2\right)^{10}=9^{10}+36^{10}+64^{10}\)

Vì \(8< 9\)\(\Rightarrow8^{10}< 9^{10}\)

mà \(27< 36\)\(\Rightarrow27^{10}< 36^{10}\)

\(\Rightarrow8^{10}+27^{10}< 9^{10}+36^{10}\)

\(\Rightarrow8^{10}+27^{10}+64^{10}< 9^{10}+36^{10}+64^{10}\)

hay \(2^{30}+3^{30}+4^{30}< 3^{20}+6^{20}+8^{20}\)

so sánh: 2^30 + 3^30 + 4^30 và 3^20 + 6^20 + 8^20
2^30 = ( 2^3)^10 = 8^ 10
3^30 = (3^3)^10 = 27^10
4^30 = (4^3)^10 = 64^10
3^20 = (3^2)^10 = 9^10
6^20 = (6^2) = 36^10
8^20 = (8^2)^10 = 84^10
vì 9^10 > 8^10
36^10 > 27^10
84^10 > 64^10
=> 2^30 + 3^30 + 4^30 < 3^20 + 6^20 + 8^20

ta có: 2³⁰=(2³)¹⁰=8¹⁰

           3²⁰=(3²)¹⁰=9¹⁰

vì 8¹⁰<9¹⁰ nên 2³⁰<3²⁰

ai k mình k lại