sorry nghe h tớ gửi quá 100 tin nhắn nên nó ko cho gửi

Bài 1

a)2711>818

b)6255>1257

c)536<1124

d)32n>23n

Bài 2

a)523<6.522

b)7.213>216

c)2115<275.498

bạn ơi bạn viết rõ hơn đi số mũ bạn bấm shift 6 

a: 199^20=1568239201^5

2003^15=8036054027^5

=>199^20<2003^15

b: 3^99=27^33>27^21=11^21

Lời giải:

a. 

$199^{20}<200^{20}=(2.100)^{20}=2^{20}.10^{40}=(2^{10})^2.10^{40}< (10^4)^2.10^{40}=10^8.10^{40}=10^{48}$
$2003^{15}> 2000^{15}=(2.10^3)^{15}=2^{15}.10^{45}> 2^{10}.10^{45}> 10^3.10^{45}=10^{48}$

$\Rightarrow 199^{20}< 2003^{15}$
b.

$3^{99}=(3^9)^{11}=19683^{11}$
$11^{21}< 11^{22}=(11^2)^{11}=121^{11}$
Hiển nhiên $19683^{11}> 121^{11}$

$\Rightarrow 3^{99}> 121^{11}> 11^{21}$

2115 = (7.3)15 = 715.315

275.498 = (33)5.(72)8 = 315.716 = 7.315.715 > 315.715 = 2115

=> 275.498 > 2115.

tick cho mink nhé 😊

72^45-72^44=72^44(72-1)=72^44*71

72^44-72^43=72^43(72-1)=72^43*71

=>72^45-72^44>72^44-72^43

a, Ta có : \(8>7\)

\(\Rightarrow2^{13}.8=2^{16}>2^{13}.7\)

b, Ta có : \(199^{20}< 200^{20}=2^{60}.5^{40}\)

Mà \(2003^{15}>2000^{15}=2^{60}.2^{45}\)

Thấy : \(45>40\)

\(\Rightarrow2000^{15}>200^{20}\)

\(\Rightarrow2003^{15}>199^{20}\)

c, Ta có : \(\left\{{}\begin{matrix}202^{303}=\left(2.101\right)^{3.101}=\left(8.101^3\right)^{101}\\303^{202}=\left(3.101\right)^{2.101}=\left(9.101^2\right)^{101}\end{matrix}\right.\)

Mà \(8.101^3>9.101^2\)

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

a) Ta có: \(2^{16}=2^{13}\cdot8\)

mà \(7< 8\)

nên \(7\cdot2^{13}< 2^{16}\)

b) \(199^{20}=1568239201^5\)

\(2003^{15}=8036054027^5\)

mà \(1568239201< 8036054027\)

nên \(199^{20}< 2003^{15}\)

c) Ta có: \(202^{303}=\left(202^3\right)^{101}\)

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

mà \(202^3>303^2\)

nên \(202^{303}>303^{202}\)

\(a.10^{30}=\left(10^3\right)^{10}=1000^{10}\\ 2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

Vì 1000¹⁰ < 1024¹⁰ => 10³⁰ < 2¹⁰⁰

\(b,333^{444}=\left(111\cdot3\right)^{444}=111^{444}\cdot3^{444}=111^{444}\cdot81^{111}\\ 444^{333}=\left(111\cdot4\right)^{333}=111^{333}\cdot4^{333}=111^{333}\cdot64^{111}\)

Vì 111⁴⁴⁴ >111³³³ ; 81¹¹¹ > 64¹¹¹ => 333⁴⁴⁴ > 444³³³

mình cảm ơn

a: 24/32=3/4

9/21=3/7

mà 3/4>3/7

nên 24/32>9/21

b: 15/25=3/5

12/15=4/5

mà 3/5<4/5

nên 15/25<12/15

c: 5/6<1<6/5

d: 7/5=1+2/5

5/3=1+2/3

mà 2/5<2/3

nên 7/5<5/3

e: 16/5=96/30

17/6=85/30

mà 96>85

nên 16/5>17/6

phân số\(\frac{213}{523}\)>\(\frac{21}{52}\)

21/52=21x523/52x523=1092/27196

                          Vì 11076/27196>1092/27196 => 21/52<213/523

213/523=213x52/523x52=11076/27196

sử dụng phép quy đồng để so sánh phân số:

 \(\frac{21}{52}=\frac{213}{523}=\frac{21.523}{52.523}=\frac{11172}{27196}=\frac{2793}{6799}\)

  \(\frac{213}{523}=\frac{21}{52}=\frac{213.52}{523.52}=\frac{11076}{13075}\)Mẫu số ghi nhầm:27196

So sánh 11172 vs 11076 thì:11172>11076

Vậy 21/52>213/523

\(3^2;2^3\)

\(=9;8\)

\(=3^2>2^3\)

Có đúng ko bạn?

3 mũ 2 thì =9

2 mũ 3 = 8 

mà 9>9

-> 3mu2> 2 mũ 3

3²ⁿ và 2³ⁿ

3²ⁿ = 9ⁿ

2³ⁿ = 8ⁿ

Vì 9ⁿ > 8ⁿ nên 3²ⁿ > 2³ⁿ