which is equivalent to $256^{\frac{3}{4}}$?\no 4\no 12\no 64\no 192

Explanation:

Step1: Rewrite 256 as a power - of 2

$256 = 2^8$, so $256^{\frac{3}{4}}=(2^8)^{\frac{3}{4}}$.

Step2: Use the power - of - a - power rule

According to the rule $(a^m)^n=a^{mn}$, then $(2^8)^{\frac{3}{4}} = 2^{8\times\frac{3}{4}}$.

Step3: Calculate the exponent

$8\times\frac{3}{4}=\frac{24}{4}=6$, so $2^{8\times\frac{3}{4}}=2^6$.

Step4: Evaluate $2^6$

$2^6 = 2\times2\times2\times2\times2\times2=64$.

Answer:

C. 64