7.5 (125⅔-16½ + 343⅓ - 3)⁻½.

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

Ответ: 1