which is equivalent to $256^{\frac{3}{4}}$?\n4\n12\n64\n192

Explanation:

Step1: Rewrite 256 as a power of 4

$256 = 4^4$, so $256^{\frac{3}{4}}=(4^4)^{\frac{3}{4}}$.

Step2: Apply power - of - a - power rule

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

Step3: Calculate the exponent

$4\times\frac{3}{4}=3$, so $4^{4\times\frac{3}{4}} = 4^3$.

Step4: Evaluate $4^3$

$4^3=4\times4\times4 = 64$.

Answer:

C. 64