\(\left(\dfrac{3}{4}x-\dfrac{9}{16}\right)\left(1.5+\dfrac{-3}{5}:x\right)=0\left(x\ne0\right)\\ TH1:\dfrac{3}{4}x-\dfrac{9}{16}=0\\ =>\dfrac{3}{4}x=\dfrac{9}{16}\\ =>x=\dfrac{9}{16}:\dfrac{3}{4}=\dfrac{3}{4}\left(tm\right)\\ TH2:1,5+\dfrac{-3}{5}:x=0\\ =>\dfrac{3}{5}:x=\dfrac{3}{2}\\ =>x=\dfrac{3}{5}:\dfrac{3}{2}=\dfrac{2}{5}\left(tm\right)\)

\(x=\dfrac{3}{4}\) và \(x=\dfrac{2}{5}\)

\(\dfrac{1}{4}\cdot\dfrac{1}{4}\cdot\dfrac{3}{4}-2\dfrac{1}{4}:1,\left(3\right)\)

\(=\dfrac{3}{64}-\dfrac{9}{4}:\dfrac{4}{3}\)

\(=\dfrac{3}{64}-\dfrac{27}{16}=\dfrac{3}{64}-\dfrac{108}{64}=-\dfrac{105}{64}\)

\(\dfrac{2}{3}+\dfrac{7}{4}:x=\dfrac{5}{6}\\ \Rightarrow\dfrac{7}{4}:x=\dfrac{5}{6}-\dfrac{2}{3}\\\Rightarrow\dfrac{7}{4}:x=\dfrac{1}{6} \\ \Rightarrow x=\dfrac{7}{4}:\dfrac{1}{6}\\ \Rightarrow x=\dfrac{21}{2}\)

Vậy \(x=\dfrac{21}{2}\)

\(\dfrac{2}{3}+\dfrac{7}{4}:x=\dfrac{5}{6}\)

=> \(\dfrac{7}{4}:x=\dfrac{5}{6}-\dfrac{2}{3}\)

=> \(\dfrac{7}{4}:x=\dfrac{5}{6}-\dfrac{4}{6}\)

=> \(\dfrac{7}{4}:x=\dfrac{1}{6}\)

=> \(x=\dfrac{7}{4}:\dfrac{1}{6}\)

=> x = \(\dfrac{7}{4}.6\)

=> \(x=\dfrac{21}{2}\)

Vậy ...

`2+4+6+...+300`

`(300+2) . [(300-2):2+1] : 2`

`= 302 . (298 : 2 + 1) : 2`

`= 302 . (149 + 1) : 2`

`= 302 . 150 : 2`

`= 22650``

Số số hạng là \(\dfrac{300-2}{2}+1=\dfrac{298}{2}+1=150\left(số\right)\)

Tổng của dãy số là (300+2)x150:2=302x75=22650

`x` thuộc `Ư(14) =` {`-14;-7;-2;-1;1;2;7;14`}

Mà `2 ≤ x ≤ 8`

`=> x` thuộc {`2;7;14`}

Vậy ` x` thuộc {`2;7;14`}

Sửa bài: 

x thuộc {2;7}

\(A=3+3^2+3^3+...+3^{99}\)

\(A=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...+\left(3^{97}+3^{98}+3^{99}\right)\)

`A =` \(\left(3+3^2+3^3\right).\left(1+3^3+...+3^{96}\right)\)

`A =` \(39.\left(1+3^3+...+3^{96}\right)\)

Mà `39 ⋮ 13`

`=> A  ⋮ 13` (đpcm)

Câu 1: D

Câu 2: D

Câu 3: A 

Câu 4: A 

Đáp án

Câu 1 : Chọn D

Câu 2 : Chọn D

Câu 3 : Chọn A

Câu 4 : Chọn A

@ChiDung

\(\dfrac{5^4.18^4}{125.9^5.16}\\ =\dfrac{5^4.\left(2.3^2\right)^4}{5^3.\left(3^2\right)^5.2^4}\\ =\dfrac{5^4.2^4.3^8}{5^3.2^4.3^{10}}\\ =\dfrac{5}{3^2}\\ =\dfrac{5}{9}\)