\(a,x:\left(-\frac{1}{2}\right)^3=-\frac{1}{2}\)

                     \(x=\left(-\frac{1}{2}\right)\times\left(-\frac{1}{2}\right)^3\)

                     \(x=\left(-\frac{1}{2}\right)^4\)

                     \(x=\frac{1}{16}\)

\(b,\left(x-2\right)^2=1\)

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

\(\Rightarrow x-2=1\)

\(\Rightarrow x=1+2\)

\(\Rightarrow x=3\)

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

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

\(\Rightarrow2x-1=2\)

\(\Rightarrow2x=2+1\)

\(\Rightarrow2x=3\)

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