`(3x + 1)^4 =` \(\dfrac{1}{16}\)

`=> (3x + 1)^4 =` \(\left(\dfrac{1}{2}\right)^4\)

`=> 3x + 1 =` \(\dfrac{1}{2}\) hoặc `3x + 1 =` \(-\dfrac{1}{2}\)

`=> 3x =` \(-\dfrac{1}{2}\) hoặc `3x =` \(-\dfrac{3}{2}\)

`=> x =` \(-\dfrac{1}{6}\) hoặc `x =` \(-\dfrac{1}{2}\)

Vậy `x =` \(-\dfrac{1}{6}\) hoặc `x =` \(-\dfrac{1}{2}\)

`123 : x - 23 : x = 20`

`=> (123 - 23) : x = 20`

`=> 100 : x = 20`

`=> x = 100 : 20`

`=> x = 5`

Vậy `x = 5`

`13 . (y + 3) - 9.( y+5) + (y+7) = 100`

`=> 13y + 39 - 9y - 45 + y+7 = 100`

`=> (13y - 9y  + y)+ 39 - 45+7 = 100`

`=> 5y + 1 = 100`

`=> 5y = 100 - 1`

`=> 5y = 99`

`=> y =` \(\dfrac{99}{5}\)

`A = 142 - [50-(2^3 - 10 - 2^3 . 5)]`

`A = 142 - [50-(8 - 10 - 8 . 5)]`

`A = 142 - [50-(-2 - 40)]`

`A = 142 - [50-(-42)]`

`A = 142 - (50+42)`

`A = 142 - 50-42`

`A = (142 - 42) - 50`

`A = 100 - 50`

`A = 50`

`(7 + 5y) : 2 + 13 = 19`

`=> (7 + 5y) : 2 = 19 - 13`

`=> (7 + 5y) : 2 = 6`

`=> 7 + 5y = 6 . 2`

`=> 7 + 5y = 12`

`=> 5y = 12 - 7`

`=> 5y = 5`

`=> y = 5 : 5`

`=> y = 1`

\(\dfrac{28^9.30^9}{105^9}=\left(\dfrac{4.7.15.2}{105}\right)^9=\left(\dfrac{4.105.2}{105}\right)^9=8^9\)

C = \(2+2^2+...+2^{100}\)

2C =\(2^2+2^3+...+2^{101}\)

2C - C = \(\left(2^2+2^3+...+2^{101}\right)-\left(2+2^2+...+2^{100}\right)\)

C = \(2^{101}-2\)

`5n + 12 ⋮ n - 5`

`=> 5n - 25 + 37  ⋮ n - 5`

`=> 5(n - 5) + 37  ⋮ n - 5`

Do `n+5  ⋮ n - 5 `

`=> 5(n+5)  ⋮ n - 5`

`=> 37  ⋮ n - 5`

`=> n - 5` thuộc `Ư(37) =` {`-37;-1;1;37`}

`=> n` thuộc {`-32;4;6;42`}

Mà `n` thuộc `N`

`=> n` thuộc {`4;6;42`}

Vậy ...

\(\dfrac{2^8.2^{18}}{8^5.4^6}=\dfrac{2^{8+18}}{\left(2^3\right)^5.\left(2^2\right)^6}=\dfrac{2^{26}}{2^{15}.2^{12}}=\dfrac{2^{26}}{2^{15+12}}=\dfrac{2^{26}}{2^{27}}=\dfrac{2^{26}}{2^{26}.2}=\dfrac{1}{2}\)

`3^2 + 4^2 + 12^2`

`= 9 + 16 + 144`

`= 25 + 144`

`= 169`

`= 13^2`