Find $(4^4 \div 4^3) \cdot 2^8$.
Performing the arithmetic in the parentheses first, we obtain $4^4 \div 4^3 = 4$, so we have \[(4^4 \div 4^3) \cdot 2^8 = 4\cdot 2^8.\]Since  $4 = 2^2$, we have  \[4\cdot 2^8 = 2^2 \cdot 2^8 = 2^{10}= \boxed{1024}.\]
1024
Level 1
Prealgebra
Problem: Find $(4^4 \div 4^3) \cdot 2^8$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To solve the expression, first simplify the division of the powers of 4. The expression $4^4 \div 4^3$ can be rewritten using the property of exponents that states $a^m \div a^n = a^{m-n}$. Thus, $4^4 \div 4^3 = 4^{4-3} = 4^1 = 4$.

Next, we need to multiply this result by $2^8$. To do this, we can express 4 in terms of base 2. Since $4 = 2^2$, we can substitute this into our expression. Therefore, we have $4 \cdot 2^8 = 2^2 \cdot 2^8$.

Now, we apply the property of exponents again, which states that $a^m \cdot a^n = a^{m+n}$. This gives us $2^2 \cdot 2^8 = 2^{2+8} = 2^{10}$.

Finally, we calculate $2^{10}$. The value of $2^{10}$ is known to be 1024. Thus, the final answer is 1024.<|END_OF_LATENT|> The final answer is $1024$.