先化简，再求值： $(1)\dfrac{1}{2}m-2\left(m-\dfrac{1}{3}{{n}^{2}}\right)-\left(\dfrac{3}{2}m-\dfrac{1}{3}{{n}^{2}}\right)$，其中$m=\dfrac{1}{3}$，$n=-1.(2)4x{{y}^{2}}-\dfrac{1}{2}({{x}^{3}}y+4x{{y}^{2}})-2\left[\dfrac{1}{4}{{x}^{3}}y-({{x}^{2}}y-x{{y}^{2}})\right]$，其中$x=\dfrac{\text{1}}{\text{2}}$，$y=-2.$

1. 对代数式进行去括号和合并同类项化简

原式 = \dfrac{1}{2}m - 2m + \dfrac{2}{3}n^2 - \dfrac{3}{2}m + \dfrac{1}{3}n^2 \
= \left(\dfrac{1}{2} - 2 - \dfrac{3}{2}\right)m + \left(\dfrac{2}{3} + \dfrac{1}{3}\right)n^2 \
= -3m + n^2

2. 代入已知的变量值进行计算

当 $m = \dfrac{1}{3}$，$n = -1$ 时，
原式 = -3 \times \dfrac{1}{3} + (-1)^2 \
= -1 + 1 \
= 0

1. 对代数式进行多层去括号和合并同类项化简

原式 = 4xy^2 - \dfrac{1}{2}x^3y - 2xy^2 - 2\left[\dfrac{1}{4}x^3y - x^2y + xy^2\right] \
= 4xy^2 - \dfrac{1}{2}x^3y - 2xy^2 - \dfrac{1}{2}x^3y + 2x^2y - 2xy^2 \
= -x^3y + 2x^2y

2. 将已知的变量值代入化简后的最简式求值

当 $x = \dfrac{1}{2}$，$y = -2$ 时，
原式 = -\left(\dfrac{1}{2}\right)^3 \times (-2) + 2 \times \left(\dfrac{1}{2}\right)^2 \times (-2) \
= -\dfrac{1}{8} \times (-2) + 2 \times \dfrac{1}{4} \times (-2) \
= \dfrac{1}{4} - 1 \
= -\dfrac{3}{4}