化简求值： $(1)0.{064}^{- \frac{1}{3}}-( \dfrac{1}{8}{)}^{0}+{16}^{ \frac{3}{4}}+0.{25}^{ \frac{1}{2}} (2)\dfrac{1}{2} \lg 25+\lg 2+( \dfrac{1}{3}{)}^{{\log }_{3}2} -\log _{2}9×\log _{3}2.$

1. 将各底数写成幂的形式，应用指数运算法则逐项化简

分别对各加项进行化简：
0.064^{-rac{1}{3}} = \left(0.4^3\right)^{-rac{1}{3}} = 0.4^{-1} = \frac{5}{2}
$\left(\frac{1}{8}\right)^0 = 1$
$16^{\frac{3}{4}} = \left(2^4\right)^{\frac{3}{4}} = 2^3 = 8$
$0.25^{\frac{1}{2}} = \left(0.5^2\right)^{\frac{1}{2}} = 0.5 = \frac{1}{2}$

2. 将化简后的数值代回原式求和

原式 $= \frac{5}{2} - 1 + 8 + \frac{1}{2} = \left(\frac{5}{2} + \frac{1}{2}\right) - 1 + 8 = 3 - 1 + 8 = 10$

1. 利用对数运算性质、对数恒等式及换底公式化简各个对数项

分别化简各项：

1. $\frac{1}{2} \lg 25 + \lg 2 = \lg\left(25^{\frac{1}{2}}\right) + \lg 2 = \lg 5 + \lg 2 = \lg(5 \times 2) = \lg 10 = 1$
2. $\left(\frac{1}{3}\right)^{\log_3 2} = \left(3^{-1}\right)^{\log_3 2} = 3^{-\log_3 2} = 3^{\log_3 \left(2^{-1}\right)} = 2^{-1} = \frac{1}{2}$
3. $\log_2 9 \times \log_3 2 = \log_2\left(3^2\right) \times \log_3 2 = 2 \log_2 3 \times \log_3 2 = 2 \times 1 = 2$

2. 将各项化简结果代回原式计算最终值

原式 $= 1 + \frac{1}{2} - 2 = -\frac{1}{2}$