[tex]Use\\\\\sqrt[n]{a}=a^{\frac{1}{n}}\\\\\left(a^m\right)^n=a^{m\cdot n}\\---------------------\\\\\left(\sqrt[3]{2^5}\right)^{\frac{1}{4}}=\left[\left(2^5\right)^\frac{1}{3}\right]^\frac{1}{4}=2^{5\cdot\frac{1}{3}\cdot\frac{1}{4}}=\boxed{2^\frac{5}{12}}\\\\Answer:\ \boxed{\boxed{\big2^{\frac{5}{12}}}}[/tex]
