Найдите значение выражения $$7\cdot \sqrt[256]{256}-\sqrt[256]{256}$$.

$$7\cdot \sqrt[256]{256}-\sqrt[256]{256} = 7 \cdot 2^{\frac{1}{8}}-2^{\frac{1}{8}} = (7-1) \cdot 2^{\frac{1}{8}} = 6 \cdot 2^{\frac{1}{8}}$$

$$\sqrt[256]{256} = 256^{\frac{1}{256}} = (2^8)^{\frac{1}{256}} = 2^{\frac{8}{256}} = 2^{\frac{1}{32}}$$

$$7\cdot 2^{\frac{1}{32}}-2^{\frac{1}{32}} = (7-1) \cdot 2^{\frac{1}{32}} = 6 \cdot 2^{\frac{1}{32}}$$.

$$\sqrt[256]{256} = 256^{\frac{1}{256}} = (2^8)^{\frac{1}{256}} = 2^{\frac{8}{256}} = 2^{\frac{1}{32}}$$

$$7\cdot \sqrt[256]{256}-\sqrt[256]{256} = 7\cdot 2^{\frac{1}{32}}-2^{\frac{1}{32}} = (7-1) \cdot 2^{\frac{1}{32}} = 6 \cdot 2^{\frac{1}{32}}$$

Ответ: $$6 \cdot 2^{\frac{1}{32}}$$.