Evaluate the following expression using the order of operations. \( 4+10(5-3) \div 4+6^{2} \) \( \begin{array}{l}18 \\ 45 \\ 42 \\ 21\end{array} \) \( \begin{array}{l}18 \\ 2\end{array} \)

To evaluate the expression \( 4 + 10(5 - 3) \div 4 + 6^{2} \), we begin by following the order of operations—often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). 1. **Parentheses**: Calculate \( 5 - 3 = 2 \). Now the expression looks like this: \( 4 + 10 \cdot 2 \div 4 + 6^{2} \). 2. **Exponents**: Calculate \( 6^{2} = 36 \). Now the expression is: \( 4 + 10 \cdot 2 \div 4 + 36 \). 3. **Multiplication and Division (from left to right)**: First, calculate \( 10 \cdot 2 = 20 \). Now it looks like this: \( 4 + 20 \div 4 + 36 \). Next, calculate \( 20 \div 4 = 5 \). Now the expression is: \( 4 + 5 + 36 \). 4. **Addition (from left to right)**: First, calculate \( 4 + 5 = 9 \). Then calculate \( 9 + 36 = 45 \). Therefore, the final result of the expression is \( 45 \). The correct answer is \( 45 \).