\(\left(2x-1\right)^3=8\)

\(\Rightarrow\left(2x-1\right)^3=2^3\)

\(\Rightarrow2x-1=2\)

\(\Rightarrow2x=3\)

\(\Rightarrow x=\dfrac{3}{2}\)

Vậy \(x=\dfrac{3}{2}\).

\(\left(x-2\right)^2=16\)

\(\Rightarrow\left(x-2\right)=\left(\pm4\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}x-2=4\\x-2=-4\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=6\\x=-2\end{matrix}\right.\)

Vậy \(x=6;x=-2\).

\(\left(n+4\right)⋮\left(n+1\right)\)

\(\Leftrightarrow\left(n+1\right).3⋮\left(n+1\right)\)

Ta có: \(\left(n+1\right)⋮\left(n+1\right)\)

\(\Rightarrow\left(n+1\right)\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)

\(\Rightarrow\left[{}\begin{matrix}n+1=1\\n+1=-1\\n+1=3\\n+1=-3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}n=0\\n=-2\\n=2\\n=-4\end{matrix}\right.\)

Mà \(n\) là số tự nhiên

\(\Rightarrow n=0;n=2\).

\(3^2.\left\{450:\left[200-\left(17+23\right)^5:50^4\right]\right\}\)

\(=9.\left\{450:\left[200-40^5:50^4\right]\right\}\)

\(=9.\left\{450:\left[200-\dfrac{2048}{125}\right]\right\}\)

\(=9.\left\{450:\dfrac{22952}{125}\right\}\)

\(=9.2,450766818\)

\(=22,05690136\).

2^x+1 = 32

2^x+1 = 2⁵

x + 1 = 5

x = 4

2^x+1 = 32

2^x+1 = 2⁵

=> x + 1 = 5

x = 5 - 1

x = 4

vì 480 ⋮ a; 720 ⋮ a mà a là lớn nhất nên a là ước chung lớn nhất của 480 và 720

480 = 2⁵.3.5

720 = 2⁴.3².5

ƯCLN( 480 , 720 ) = 2⁴.3.5= 240 

vậy a = 240 

300 : { 180 - ( 34 + (15 -3)² }

300 : { 180 - ( 34 + 144)}

300 : { 180 - 178}

300 : 2

= 150