7. (125⁻²/³ - 16²/⁴ + 343¹/³ - 3)⁻¹/².

7. $$ (125^{-\frac{2}{3}} - 16^{\frac{2}{4}} + 343^{\frac{1}{3}} - 3)^{-\frac{1}{2}} = ( (5^3)^{-\frac{2}{3}} - (2^4)^{\frac{2}{4}} + (7^3)^{\frac{1}{3}} - 3)^{-\frac{1}{2}} = (5^{-2} - 2^2 + 7 - 3)^{-\frac{1}{2}} = (\frac{1}{25} - 4 + 7 - 3)^{-\frac{1}{2}} = (\frac{1}{25})^{-\frac{1}{2}} = (\frac{1}{25})^{-\frac{1}{2}} = (\frac{1}{\sqrt{\frac{1}{25}}}) = (\frac{1}{\frac{1}{5}}) = 5 $$.

Ответ: 5