To simplify the expression [tex]\(4 - 16 \div 4 + 4^2\)[/tex], we will follow the order of operations, often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
1. Division: First, we perform the division operation:
[tex]\[
16 \div 4 = 4
\][/tex]
So the expression simplifies to:
[tex]\[
4 - 4 + 4^2
\][/tex]
2. Exponentiation: Next, we perform the exponentiation operation:
[tex]\[
4^2 = 16
\][/tex]
Now the expression becomes:
[tex]\[
4 - 4 + 16
\][/tex]
3. Subtraction and Addition: Finally, we perform the addition and subtraction from left to right:
[tex]\[
4 - 4 = 0
\][/tex]
[tex]\[
0 + 16 = 16
\][/tex]
Therefore, the simplified result of the expression [tex]\(4 - 16 \div 4 + 4^2\)[/tex] is:
[tex]\[
\boxed{16}
\][/tex]
