$a){\left({\left(-4,2\right)}^5\right)}^3={\left(-4,2\right)}^{5\cdot 3}={\left(-4,2\right)}^{15}$  

$b){\left({\left(0,15\right)}^4\right)}^{-3}={\left(0,15\right)}^{4\cdot \left(-3\right)}={\left(0,15\right)}^{-12}$  

$c){\left({\left(9^{-7}\right)}^{-3}\right)}^2={\left(9^{-7}\right)}^{-3\cdot 2}={\left(9^{-7}\right)}^{-6}=9^{-7\cdot \left(-6\right)}=9^{42}$  

$d){\left({\left({\left(-\frac{1}{4}\right)}^{-1}\right)}^{-2}\right)}^{-3}={\left({\left(-\frac{1}{4}\right)}^{-1}\right)}^{-2\cdot \left(-3\right)}={\left({\left(-\frac{1}{4}\right)}^{-1}\right)}^6={\left(-\frac{1}{4}\right)}^{-1\cdot 6}={\left(-\frac{1}{4}\right)}^{-6}$