$\text{a)}$

${\left(\frac{1}{4}\right)}^{-7}=4^7$

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

$\underline{\underline{{\left(\frac{1}{4}\right)}^{-7}>4^2\cdot {\left(\frac{1}{4}\right)}^{-4}}}$

 

$\text{b)}$

${\left(-2\right)}^{-3}\cdot {\left(-\frac{1}{2}\right)}^4={\left(-\frac{1}{2}\right)}^3\cdot {\left(-\frac{1}{2}\right)}^4=$ ${\left(-\frac{1}{2}\right)}^7$

${\left(-2\right)}^{-1}=-\frac{1}{2}$

$\underline{\underline{{\left(-2\right)}^{-3}\cdot {\left(-\frac{1}{2}\right)}^4>{\left(-2\right)}^{-1}}}$

 

$\text{c)}$

$5\cdot {\left(\frac{1}{5}\right)}^{-3}=5\cdot 5^3=5^4$

${\left(0,2\right)}^{-4}\cdot 5^{-1}={\left(\frac{1}{5}\right)}^{-4}\cdot 5^{-1}=$ $5^4\cdot 5^{-1}=5^3$

$\underline{\underline{5\cdot {\left(\frac{1}{5}\right)}^{-3}>{\left(0,2\right)}^{-4}\cdot 5^{-1}}}$

 

$\text{d)}$

$6^{-3}\cdot {\left(-\frac{1}{6}\right)}^2={\left(\frac{1}{6}\right)}^3\cdot {\left(\frac{1}{6}\right)}^2={\left(\frac{1}{6}\right)}^5$

${\left(-6\right)}^{-2}\cdot {\left(\frac{1}{6}\right)}^3={\left(-\frac{1}{6}\right)}^2\cdot {\left(\frac{1}{6}\right)}^3={\left(\frac{1}{6}\right)}^5$

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