### Instruction: If $(2^3)^{(2^3)} = 2^N$, what is the value of $N$?### Response: To solve this problem, I need to apply the rules of exponents for powers of powers.
I know that $(a^b)^c = a^{bc}$, so I can rewrite the left-hand side of the equation as $2^{(3 \cdot 2^3)}$.
Now, I have $2^{(3 \cdot 2^3)} = 2^N$, which means that the exponents must be equal.
So, I need to solve for $N$ in the equation $3 \cdot 2^3 = N$.
I can simplify the left-hand side by multiplying $3$ and $2^3$, which gives me $3 \cdot 2^3 = 3 \cdot 8 = 24$.
So, I have $24 = N$, which is the answer.