\[27^{\frac{2}{3}} - \left( \frac{1}{16} \right)^{- \frac{3}{4}} - \left( \sqrt[4]{49} \right)^{2} =\]
\[= \left( 3^{3} \right)^{\frac{2}{3}} - \left( 2^{- 4} \right)^{- \frac{3}{4}} - \sqrt[4]{7^{4}} =\]
\[= 3^{2} - 2^{3} - 7 =\]
\[= 9 - 8 - 7 = - 6\]