Plot[1.88 (a^(1/3)) , {a,-0.56,0.56}]
I unable to plot the expression in x axes and variable in y axes
I'm not 100% sure I got what you are asking, but maybe this is what you are looking for:
ParametricPlot[{1.88 (a^(1/3)), a}, {a, -0.56, 0.56}]
You have a varying on the y axis and 1.88 (a^(1/3)) varying on the x axis.