Find $1^{234} + 4^6 \div 4^4$.
To simplify this expression, I will use the properties of exponents and order of operations. First, I notice that $1^{234}$ is just 1, since any power of 1 is 1. So I can rewrite the expression as $1 + 4^6 \div 4^4$. Next, I notice that $4^6 \div 4^4$ can be simplified by subtracting the exponents, since they have the same base. So I can rewrite the expression as $1 + 4^{6 - 4}$. This gives me $1 + 4^2$, which is $1 + 16$. Finally, I can add these two terms to get the answer. 