$a)$

${\left(4x\right)}^2=4^2{x}^2$  

$b)$  

${\left(-3a\right)}^5={\left(-3\right)}^5{a}^5$    

$c)$

${\left(\frac{2}{5}xz\right)}^3={\left(\frac{2}{5}\right)}^3{x}^3{z}^3$

$d)$

${\left(-1\frac{1}{2}bc\right)}^4={\left(-1\frac{1}{2}\right)}^4{b}^4{c}^4$

$e)$

${\left(1.2mn\right)}^7={\left(1.2\right)}^7{m}^7{n}^7$

$f)$

${\left(-0.3abc\right)}^3={\left(-0.3\right)}^3{a}^3{b}^3{c}^3$