$\sqrt{2}(\sqrt{50}-4^{\frac{1}{4}})+8^{-\frac{2}{3}}=\sqrt{100}- 2^{\frac{1}{2}}\times 4^{\frac{1}{4}}+2^{-2}=10-2^{\frac{1}{2}}\times 2^{\frac{1}{2}}+\frac{1}{4}=10-2+\frac{1}{4}=8+\frac{1}{4}=\frac{33}{4} $