\(2^n\cdot16-2^{n+1}=2^6-2^3\\ 2^n\cdot16-2^n\cdot2= 2^3\cdot\left(8-1\right)\\ 2^n\cdot\left(16-2\right)=8\cdot7\\ 2^n\cdot14=8\cdot7\\ 2^n\cdot\left(14:7\right)=8\\ 2^n\cdot2=8\\ 2^{n+1}=2^3\\ =>n+1=3\\ n=3-1\\ n=2\)

\(A=1^2+2^2+3^2+....+10^2\\ A=1^{ }+\left(1+1\right)\cdot2+3\cdot\left(2+1\right)+.....+10\cdot\left(9+1\right)\\ A=1+2\cdot1+2+3\cdot2+3+....+10\cdot9+10\\ A=\left(1+2+3...+10\right)+\left(1\cdot2+3\cdot2+.....+10\cdot9\right)\)

Gọi 1+2+3+...+10 là P

Số số hạng là: (10 - 1) : 1 +1 = 10 (số)

P = (10+1) . 10 : 2 = 55 

P = 55

Gọi \(1\cdot2+2\cdot3+....+9\cdot10\)  là C

\(C=1\cdot2+2\cdot3+....+9\cdot10\\ 3\cdot C=1\cdot2\cdot3+2\cdot3\cdot3+....+9\cdot10\cdot3\\ 3\cdot C=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+....+9\cdot10\cdot\left(11-8\right)\\ 3\cdot C=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+.....+9\cdot10\cdot11-8\cdot9\cdot10\\ 3\cdot C=9\cdot10\cdot11\\ 3\cdot C=990\\ C=330\)

\(=>A=P+C\\ =>A=55+330\\ A=385\)

b)

\(B=5^2+10^2+15^2+...+50^2\\ B=5^2+\left(2\cdot5\right)^2+\left(3\cdot5\right)^2+....+\left(5\cdot10\right)^2\\ B=5^2+2^2\cdot5^2+3^2\cdot5^2+...+5^2\cdot10^2\\ B=5^2\cdot\left(1+2^2+3^2+....+10^2\right)\\ B=25\cdot\left(1+2^2+3^2+....+10^2\right)\)

\(\left(1+2^2+3^2+....+10^2\right)=A\)

\(=>B=25\cdot A\\ B=25\cdot385\\ B=9625\)

\(\dfrac{3}{4}:x=1\dfrac{1}{2}\)

\(x=\dfrac{3}{4}\times\dfrac{2}{3}\)

\(x=\dfrac{1}{2}\)

\(\dfrac{5}{8}-x\)

\(=>\dfrac{5}{8}-\dfrac{1}{2}=\dfrac{5}{8}-\dfrac{4}{8}=\dfrac{1}{8}\)

\(A=2023\times2024\\ =\left(2022+1\right)\times2024\\ =2022\times2024+2024\\ B=2022\times2025\\ =2022\times\left(2024+1\right)\\ =2022\times2024+2022\)

Vì 2022 x 2024 = 2022 x 2024

=> 2024 > 2022

=> A> B

Cách 2

A= 2023 x 2024 = 4094552

 B = 2022 x 2025 =4094550

Vì 4094552 > 4094550 = > A> B

Hiệu 2 số là:

5 x 2 =10

Số bé là:

(210-10) : 2 =100

Số lớn là : 

210-100=110

Đ/s:

\(25\cdot x^2=25\\ x^2=25\div25\\ x^2=1\\ x^2=1^2\\ x=1\\ 8^{x-3}=1\\ 8^{x-3}=8^0\\ x-3=0\\ x=0+3\\ x=3\)

\(a,5-3\cdot x=2\\ 3\cdot x=5-2\\ 3\cdot x=3\\ x=3:3\\ x=1\\ b,5+2:x=3\\ 2:x=3-5\\ 2:x=-2\\ x=2:\left(-2\right)\\ x=-1\)

\(\dfrac{x-3}{3}=\dfrac{2x+1}{5}\\ \left(x-3\right)\cdot5=\left(2x+1\right)\cdot3\\ x5-15=6x+3\\ x5-6x=3+15\\ -x=18\\ \Rightarrow x=-18\)

\(\dfrac{x+1}{22}=\dfrac{6}{x}\\ \left(x+1\right)\cdot x=6\cdot22\\ \left(x+1\right)\cdot x=2\cdot3\cdot2\cdot11\\ \left(x+1\right)\cdot x=12\cdot11\\ \Rightarrow x=11\)

\(\dfrac{2x-1}{21}=\dfrac{3}{2x+1}\\ \left(2x-1\right)\cdot\left(2x+1\right)=21\cdot3\\ \left(2x-1\right)\cdot\left(2x+1\right)=7\cdot3\cdot3\\ \left(2x-1\right)\cdot\left(2x+1\right)=7\cdot9\\ \Rightarrow2x+1=9\\ 2x=8\\ x=4\)

\(3,527+65\times73+65\times27+3,573\\ =\left(3,527+3,573\right)+65\times\left(73+27\right)\\ =7,1+65\times100\\ =7,1+6500\\ =6507,1\)

\(A=\dfrac{2019\times2020-3038}{2018\times2019+1000}\)

\(A=\dfrac{2019\times\left(2018+2\right)-3038}{2018\times2019+1000}\)

\(A=\dfrac{2019\times2018+2019\times2-3038}{2018\times2019+1000}\)

\(A=\dfrac{2019\times2018+4038-3038}{2019\times2018+1000}\)

\(A=\dfrac{2019\times2018+1000}{2019\times2018+1000}\)

\(A=1\)

64dm= 6,4 m

S trần nhà là:

8,5 x 6,4= 54,4 (m²)

S 4 bức tường là:

(8,5+6,4) x 2 x 3,5 = 104,3(m²)

S các cửa là:

25% x 54,4=13,6 (m²)

S quét vôi là

(104,3 - 13,6)+54,4= 145,1 (m²)