Question

упростите: √2 ∛2 ⁶√2

Answer 1

√2 = ⁶√2^3; ∛2 = ⁶√2^2.

√2 ∛2 ⁶√2 = ⁶√2^3 ⁶√2^2 ⁶√2 = ⁶√2^6 = 2.

Ответ: 2.

Answer 2

$\sqrt{2}\cdot \sqrt[3]{2}\cdot \sqrt[6]{2}=2^{\frac{1}{2}}\cdot 2^{\frac{1}{3}}\cdot 2^{\frac{1}{6}}=2^{\frac{1}{2}+\frac{1}{3}+\frac{1}{6}}=2^{\frac{6}{6}}=2^1=2$