Which is equivalent to 64 ^1/4

we have

64^{\frac{1}{4}}

we know that

64=2^{6}= 2^{2}*2^{4}

so

64^{\frac{1}{4}}=\sqrt[4]{64} \\ \\\sqrt[4]{64} =\sqrt[4]{2^{2}*2^{4}}

\sqrt[4]{2^{2}*2^{4}}=2\sqrt[4]{2^{2}}= 2\sqrt[4]{4}

therefore

the answer is the option  

2\sqrt[4]{4}