what is the value of the expression $(2^{4})^{2}$?

Explanation:

Step1: Apply power - of - a - power rule

According to the rule $(a^m)^n=a^{m\times n}$, for $(2^4)^2$, we have $m = 4$ and $n=2$. So, $(2^4)^2=2^{4\times2}$.

Step2: Calculate the exponent

$4\times2 = 8$, so $2^{4\times2}=2^8$.

Step3: Evaluate $2^8$

$2^8=2\times2\times2\times2\times2\times2\times2\times2 = 256$.

Answer:

256