\(1,\left(2x-5\right)^2=\dfrac{9}{16}\)
\(\Leftrightarrow\left|2x-5\right|=\dfrac{3}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-5=\dfrac{3}{4}\\2x-5=-\dfrac{3}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{23}{8}\\x=\dfrac{17}{8}\end{matrix}\right.\)
\(2,\left(1-2x\right)^3=-\dfrac{27}{64}\)
\(\Leftrightarrow1-2x=-\dfrac{3}{4}\)
\(\Leftrightarrow x=\dfrac{7}{8}\)
\(3,\left(3x+\dfrac{1}{2}\right)^4=0\)
\(\Leftrightarrow3x+\dfrac{1}{2}=0\)
\(\Leftrightarrow x=-\dfrac{1}{6}\)
\(4,\left(x+\dfrac{3}{4}\right)^3+5=-3\)
\(\Leftrightarrow\left(x+\dfrac{3}{4}\right)^3=-8\)
\(\Leftrightarrow x+\dfrac{3}{4}=-2\)
\(\Leftrightarrow x=-\dfrac{11}{4}\)
\(5,\left(x-\dfrac{1}{5}\right)^2=\dfrac{1}{4}\)
\(\Leftrightarrow\left|x-\dfrac{1}{5}\right|=\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{5}=\dfrac{1}{2}\\x-\dfrac{1}{5}=-\dfrac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{10}\\x=-\dfrac{3}{10}\end{matrix}\right.\)
\(6,2x=\dfrac{84}{163}\)
\(\Leftrightarrow x=\dfrac{42}{163}\)