\[8^{\frac{2}{3}} + \left( \frac{1}{25} \right)^{- \frac{1}{2}} - \left( \sqrt[4]{4} \right)^{2} =\]
\[= \left( 2^{3} \right)^{\frac{2}{3}} + \left( 5^{- 2} \right)^{- \frac{1}{2}} - \sqrt[4]{2^{4}} =\]
\[= 2^{2} + 5 - 2 = 4 + 3 = 7\]