which is equivalent to $64^{\frac{1}{4}}$?\n$2sqrt4{4}$\n$4$\n$16$\n$16sqrt4{4}$

Explanation:

Step1: Rewrite 64 as a power of 2

We know that $64 = 2^6$. So, $64^{\frac{1}{4}}=(2^6)^{\frac{1}{4}}$.

Step2: Apply power - of - a - power rule

According to the rule $(a^m)^n=a^{mn}$, we have $(2^6)^{\frac{1}{4}} = 2^{6\times\frac{1}{4}}=2^{\frac{6}{4}}=2^{\frac{3}{2}}$.

Step3: Rewrite as a radical

$2^{\frac{3}{2}}=\sqrt{2^3}=\sqrt{8}$. Another way is to rewrite 64 as $4^3$. Then $64^{\frac{1}{4}}=(4^3)^{\frac{1}{4}}$.

Step4: Apply power - of - a - power rule again

$(4^3)^{\frac{1}{4}} = 4^{3\times\frac{1}{4}}=4^{\frac{3}{4}}=\sqrt[4]{4^3}=\sqrt[4]{64}= \sqrt[4]{16\times4}=2\sqrt[4]{4}$.

Answer:

$2\sqrt[4]{4}$