$\text{a)}$

$\frac{2^{-2}}{3^{-2}}={\left(\frac{2}{3}\right)}^{-2}$

$\frac{3^3}{4^3}$   $={\left(\frac{3}{4}\right)}^3$

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

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

 

$\text{b) przy załoz˙eniu a}\ne 0,\text{b}\ne 0,\text{x}\ne 0,\text{y}\ne 0$  

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

$-\frac{x^{-3}}{y^{-3}}$   $={\left(-\frac{x}{y}\right)}^{-3}$

$\frac{x^3}{y^3}$   $={\left(\frac{x}{y}\right)}^3$

$\frac{{\left(-a\right)}^4}{b^4}$   $={\left(-\frac{a}{b}\right)}^4$

 

$\text{c) przy załoz˙eniu x}\ne 0,\text{y}\ne 0$

$\frac{{\left(2x\right)}^3}{{\left(3y\right)}^3}$   $={\left(\frac{2x}{2y}\right)}^3={\left(\frac{x}{y}\right)}^3$

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

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

$-\frac{x^{-8}}{-y^{-8}}$   $=-{\left(-\frac{x}{y}\right)}^{-8}$

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