$=\sqrt{2}\sqrt[4]{2}$
Apply radical rule $\sqrt{a}=a^{\frac{1}{2}}$$=2^{\frac{1}{2}}\sqrt[4]{2}$
Apply radical rule $\sqrt[n]{a}=a^{\frac{1}{n}}$$=2^{\frac{1}{2}}\cdot 2^{\frac{1}{4}}$
Apply exponent rule $a^b\cdot a^c=a^{b+c}$$=2^{\frac{1}{2}+\frac{1}{4}}$
Apply radical rule $\sqrt{ab}=\sqrt{a}\sqrt{b},\quad a\ge0, b\ge0$$=\sqrt{2}\sqrt{\sqrt{2}}$
$2^{\frac{3}{4}}=\sqrt[4]{2^{3}}$$=\sqrt[4]{2^{3}}$