$$1^{-1}+2^{-2}+3^{-3}+{\left(-1\right)}^{-1}+{\left(-2\right)}^{-2}+{\left(-3\right)}^{-3}$$

$$=\frac{1}{1^1}+\frac{1}{2^2}+\frac{1}{3^3}+{\left(-\frac{1}{1}\right)}^1+{\left(-\frac{1}{2}\right)}^2+{\left(-\frac{1}{3}\right)}^3$$

$$=\bcancel{\frac{1}{1}}+\frac{1}{4}+\cancel{\frac{1}{27}}-\bcancel{\frac{1}{1}}+\frac{1}{4}-\cancel{\frac{1}{27}}$$

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

$$=\frac{2}{4}$$