\[{\text{Вычислите: }}{\left( {\sqrt[3]{{\sqrt 8 }}} \right)^2}.\]
\[\begin{array}{l}\sqrt[n]{a} = {a^{\frac{1}{n}}}\\{\left( {{a^x}} \right)^y} = {a^{x \cdot y}}\end{array}\]
\[\begin{array}{l}{\left( {\sqrt[3]{{\sqrt 8 }}} \right)^2} = {\left( {{{\left( {{8^{\frac{1}{2}}}} \right)}^{\frac{1}{3}}}} \right)^2} = {\left( {{{\left( {{{\left( {{2^3}} \right)}^{\frac{1}{2}}}} \right)}^{\frac{1}{3}}}} \right)^2} = \\{\left( {{{\left( {{2^{\frac{3}{2}}}} \right)}^{\frac{1}{3}}}} \right)^2} = {\left( {{2^{\frac{1}{2}}}} \right)^2} = 2\end{array}\]
\[2\]
