Ta có : 

3¹⁷ = 3¹⁶ . 3

= 3^4.4 . 3

= ( 3⁴ )⁴ . 3

= 81⁴ . 3 > 61⁴ . 3 > 61⁴

Vậy 3¹⁷ > 61⁴

a)\(2x+3\left(x+4\right)-14=8\)

\(2x+3x+12-14=8\)

\(2x+3x-2=8\)

\(5x-2=8\)

\(5x=8+2\)

\(5x=10\)

\(x=10:5\)

\(x=2\)

b)\(x+2x+3x=4x+16\)

\(x\left(1+2+3\right)=4x+16\)

\(6x-4x=16\)

\(2x=16\)

\(x=16:2\)

\(x=8\)

\(\frac{x-1}{3}-\frac{1}{y+2}=\frac{1}{6}\)

\(\Leftrightarrow\frac{\left(x-1\right)\left(y+2\right)-3}{3\left(y+2\right)}=\frac{1}{6}\)

\(\Leftrightarrow2\left(x-1\right)\left(y+2\right)-6=\left(y+2\right)\)

\(\Leftrightarrow\left(2x-3\right)\left(y+2\right)=6\)

Vì \(x,y\)nguyên nên \(2x-3,y+2\)là các ước của \(6\)mà \(2x-3\)là số lẻ. 

Ta có bảng giá trị: 

\(\frac{1}{5}:\left(-\frac{2}{3}\right)=\frac{1}{5}\times\frac{-3}{2}=\frac{-3}{10}\)

Viết thương sau thành tích: 

\(\frac{1}{5}\)\(:\left(-\frac{2}{3}\right)\)

\(=\)\(\frac{1}{5}.-\frac{3}{2}\)

\(=\)\(\frac{-3}{10}\)

\(\frac{2}{3}-4.\left(\frac{1}{2}+\frac{3}{4}\right)\)

\(=\frac{2}{3}-4.\left(\frac{2}{4}+\frac{3}{4}\right)\)

\(=\frac{2}{3}-4.\frac{5}{4}\)

\(=\frac{2}{3}-5\)

\(=-4\frac{1}{3}\)

\(\frac{2}{3}-4\left(\frac{1}{2}+\frac{3}{4}\right)=\frac{2}{3}-4\left(\frac{2}{4}+\frac{3}{4}\right)=\frac{2}{3}-4.\frac{5}{4}\)\(\frac{5}{4}\)\(=\frac{2}{3}-\frac{5}{1}=\frac{2}{3}-\frac{15}{3}=\frac{-13}{3}\)