\[\begin{array}{l}{\left( {\frac{4}{5}} \right)^{ - 2}} = {\left( {\frac{5}{4}} \right)^2} = \frac{{25}}{{16}}\\{\left( {\frac{1}{{27}}} \right)^{\frac{1}{3}}} = \frac{{{1^{\frac{1}{3}}}}}{{{{27}^{\frac{1}{3}}}}} = \frac{1}{{\sqrt[3]{{27}}}} = \frac{1}{3}\\{379^0} = 1\\{\left( {\frac{4}{5}} \right)^{ - 2}} - {\left( {\frac{1}{{27}}} \right)^{\frac{1}{3}}} + 4 \cdot {379^0} = \frac{{25}}{{16}} - \frac{1}{3} + 4 \cdot 1 = \\\frac{{59}}{{48}} + 4 = 4 + 1\frac{{11}}{{48}} = 5\frac{{11}}{{48}}\end{array}\]

\[5\frac{{11}}{{48}}\]