$${\left(\mathrm{x}+\mathrm{y}\right)}^0+0,{25}^{-1}+{\left(-0,5\right)}^{-2}+{\left(0,{001}^0\right)}^{-4}$$

$$=1+{\left(\frac{25}{100}\right)}^{-1}+{\left(-\frac{5}{10}\right)}^{-2}+1^{-4}$$

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

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

$$=1+\frac{4}{1}+\frac{4}{1}+1$$

$$=1+4+4+1$$