Question

Найдите значение выражения (2^1/3*2^1/4)^2/6^√2

Answer 1

$\displaystyle \frac{(2^{1/3}\cdot 2^{1/4})^2}{6^{\sqrt2}}=\frac{(2^{7/12})^2}{6^{\sqrt2}}=\frac{2^{14/12}}{2^{\sqrt2}\cdot 3^{\sqrt2}}=\frac{2^{7/6}}{2^{\sqrt2}\cdot 3^{\sqrt2}}=\frac{2^{\frac{7}{6}-\sqrt2}}{3^{\sqrt2}}$

Answer 2

$\dfrac{(2^{\frac{1}{3}}\cdot2^{\frac{1}{4}})^{2} }{\sqrt[6]{2}} =\dfrac{(2^{\frac{1}{3} +\frac{1}{4} })^{2}}{2^{\frac{1}{6}}}=\dfrac{(2^{\frac{7}{12}})^{2} }{2^{\frac{1}{6}}}=\dfrac{2^{\frac{7}{6}}}{2^{\frac{1}{6}}} =2^{\frac{7}{6}-\frac{1}{6}}=2^{\frac{6}{6} } =\boxed2\\\\Otvet:\boxed2$