Bài 1:

a) Ta có: \(1000\cdot25\cdot4\)

\(=10^3\cdot10^2\)

\(=10^5\)

b) Ta có: \(32\cdot24\cdot243\)

\(=2^5\cdot2^3\cdot3\cdot3^5\)

\(=2^8\cdot3^6\)

\(=6^6\cdot2^2\)

\(=\left(6^3\right)^2\cdot2^2\)

\(=\left(6^3\cdot2\right)^2=432^2\)

c) Ta có: \(8\cdot9\cdot10\cdot125\)

\(=2^3\cdot3^2\cdot2\cdot5\cdot5^3\)

\(=2^4\cdot3^2\cdot5^4\)

\(=\left(10^2\right)^2\cdot3^2\)

\(=\left(10^2\cdot3\right)^2\)

\(=300^2\)

d) Ta có: \(6^{15}\cdot6^{21}\cdot36\)

\(=6^{15}\cdot6^{21}\cdot6^2\)

\(=6^{38}\)

e) Ta có: \(\frac{5^{2019}}{5^{2000}}\cdot625\)

\(=5^{19}\cdot5^4=5^{23}\)

Bài 2:

a) Ta có: 57<75

nên \(29^{57}< 29^{75}\)

`a,`

`5/6=1-1/6`

`7/8=1-1/8`

Mà `1/6>1/8 -> 5/6<7/8`

`b,`

`9/5=(9 \times 2)/(5 \times 2)=18/10`

`3/2=(3 \times 5)/(2 \times 5)=15/10`

`18/10 > 15/10 -> 9/5 > 3/2`

`c,`

`2017/2018 = 1-1/2018`

`2019/2020=1-1/2020`

`1/2018 > 1/2020 -> 2017/2018 < 2019/2020`

`d,`

`2018/2017 = 1+1/2017`

`2020/2019 = 1+1/2019`

`1/2017 > 1/2019 -> 2018/2017>2020/2019`

a 

oki

a: 21^15=3^15*7^15

27^5*49^8=3^15*7^14

mà 15>14

nên 21^15>27^5*49^8

b: \(2020^{2020}-2020^{2019}=2020^{2019}\left(2020-1\right)=2020^{2019}\cdot2019\)

\(2020^{2019}-2020^{2018}=2020^{2018}\cdot2019\)

mà 2019>2018

nên 2020^2020-2020^2019>2020^2019-2020^2018

\(\frac{2020}{2019}\)bé hơn \(\frac{2021}{2020}\)

vì 2020 bé hơn 2021

2019 nhỏ hơn 2020

2020/2019<2021/2020

mọi người có thể giải và trình bày chi tiết giúp em ạ! 

Em cảm ơn

A<B

\(A=2018\times2020+2021\) và \(B=2019\times2019+2021\)

\(A=2018\times2019+2018+2021\)

\(B=2018\times2019+2019+2021\)

Vì \(2019>2018\Rightarrow A< B\)

Ta có :

2018 x 2020 = 2018 x ( 2019 + 1 ) = 2018 + 2018 x 2019 < 2019 + 2018 x 2019 = 2019 x ( 2018 + 1 )

= 2019 x 2019

=> 2018 x 2020 < 2019 x 2019

=> 2018 x 2020 + 2021 < 2019 x 2019 + 2021

=> A < B

\(A=2018.2020+2021=2018.2019+2018+2021\)

\(B=2019.2019+2021=2018.2019+2019+2021\)

\(\Rightarrow A< B\)