Đáp án:

$\begin{array}{l}
a)\dfrac{8}{5}x - \dfrac{4}{3}x = \dfrac{{ - 5}}{{16}}.\dfrac{7}{5}\\
 \Rightarrow \left( {\dfrac{8}{5} - \dfrac{4}{3}} \right).x = \dfrac{{ - 7}}{{16}}\\
 \Rightarrow \dfrac{{24 - 20}}{{15}}.x = \dfrac{{ - 7}}{{16}}\\
 \Rightarrow \dfrac{4}{{15}}.x = \dfrac{{ - 7}}{{16}}\\
 \Rightarrow x = \dfrac{{ - 7}}{{16}}.\dfrac{{15}}{4}\\
 \Rightarrow x = \dfrac{{ - 105}}{{64}}\\
\text{Vậy}\,x = \dfrac{{ - 105}}{{64}}\\
b){\left( {\dfrac{2}{3}x - \dfrac{1}{5}} \right)^2} = \dfrac{4}{9}\\
 \Rightarrow \left[ \begin{array}{l}
\dfrac{2}{3}x - \dfrac{1}{5} = \dfrac{2}{3}\\
\dfrac{2}{3}x - \dfrac{1}{5} =  - \dfrac{2}{3}
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
\dfrac{2}{3}x = \dfrac{2}{3} + \dfrac{1}{5} = \dfrac{{13}}{{15}}\\
\dfrac{2}{3}x = \dfrac{{ - 2}}{3} + \dfrac{1}{5} = \dfrac{{ - 7}}{{15}}
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
x = \dfrac{{13}}{{15}}.\dfrac{3}{2} = \dfrac{{13}}{{10}}\\
x = \dfrac{{ - 7}}{{15}}.\dfrac{3}{2} = \dfrac{{ - 7}}{{10}}
\end{array} \right.\\
\text{Vậy}\,\,x = \dfrac{{13}}{{10}};x = \dfrac{{ - 7}}{{10}}\\
c){\left( {\dfrac{1}{5} - \dfrac{3}{2}x} \right)^2} = \dfrac{9}{4} = {\left( {\dfrac{3}{2}} \right)^2}\\
 \Rightarrow \left[ \begin{array}{l}
\dfrac{1}{5} - \dfrac{3}{2}x = \dfrac{3}{2}\\
\dfrac{1}{5} - \dfrac{3}{2}x =  - \dfrac{3}{2}
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
\dfrac{3}{2}x = \dfrac{1}{5} - \dfrac{3}{2} = \dfrac{{ - 13}}{{10}}\\
\dfrac{3}{2}x = \dfrac{1}{5} + \dfrac{3}{2} = \dfrac{{17}}{{10}}
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
x = \dfrac{{ - 13}}{{15}}\\
x = \dfrac{{17}}{{15}}
\end{array} \right.\\
\text{Vậy}\,x = \dfrac{{ - 13}}{{15}};x = \dfrac{{17}}{{15}}\\
d){\left( {1,25 - \dfrac{4}{3}x} \right)^3} = 125\\
 \Rightarrow 1,25 - \dfrac{4}{3}x = 5\\
 \Rightarrow \dfrac{4}{3}x = 1,25 - 5\\
 \Rightarrow \dfrac{4}{3}x =  - 3,75\\
 \Rightarrow x =  - 3,75.\dfrac{3}{4}\\
 \Rightarrow x = \dfrac{{ - 15}}{4}.\dfrac{3}{4}\\
 \Rightarrow x = \dfrac{{ - 45}}{{16}}\\
\text{Vậy}\,x = \dfrac{{ - 45}}{{16}}\\
e){2^x} + {2^{x + 4}} = 544\\
 \Rightarrow {2^x} + {2^x}{.2^4} = 544\\
 \Rightarrow {2^x}.17 = 544\\
 \Rightarrow {2^x} = 32\\
 \Rightarrow {2^x} = {2^5}\\
 \Rightarrow x = 5\\
\text{Vậy}\,x = 5\\
f)\left| {3x - 2} \right| = \left| {2x - 3} \right|\\
 \Rightarrow \left[ \begin{array}{l}
3x - 2 = 2x - 3\\
3x - 2 =  - 2x + 3
\end{array} \right.
\end{array}$

$\begin{array}{l}
 \Rightarrow \left[ \begin{array}{l}
x =  - 1\\
5x = 5
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
x =  - 1\\
x = 1
\end{array} \right.\\
\text{Vậy}\,x =  - 1;x = 1
\end{array}$