Problem 111 - Algebra and Trigonometry

Question

Use the order of operations to simplify each expression. $$8^{2}-16 \div 2^{2} \cdot 4-3$$

Step-by-Step Solution

Answer

The simplified expression of \(8^{2}-16 \div 2^{2} \cdot 4-3\) is 45.

Step 1: Handle the Exponents

The first parts of the expression to resolve are the exponents. The only exponent present is \(8^{2}\) which results to 64. So, the expression will now appear as \(64 - 16 \div 2^{2} \cdot 4 - 3\).

Step 2: Perform Division and Multiplication

Next, handle the division and multiplication from left to right. First we divide, \(16 \div 2^{2} = 16 \div 4 = 4\). Multiply this result, 4, by 4 to get 16. Therefore, the expression simplifies to \(64 - 16 - 3\).

Step 3: Subtraction

Finally, we perform subtraction from left to right. First, subtract 16 from 64 to get 48. Then subtract 3 from 48 to get the final answer 45. Therefore, \(8^{2}-16 \div 2^{2} \cdot 4-3 = 45.\)