Evaluate the following expression.
$6+8^2 \div 4 \cdot 2^3$
$6+8^2 \div 4 \cdot 2^3=$ $\square$ (Simplify your answer.)
Answer (1)
Evaluate exponents: 8 2 = 64 and 2 3 = 8 .
Perform division: 64 ÷ 4 = 16 .
Perform multiplication: 16 × 8 = 128 .
Perform addition: 6 + 128 = 134 . The final answer is 134 .
Explanation
Understanding the Expression We need to evaluate the expression 6 + 8 2 ÷ 4 ⋅ 2 3 . To do this, we will follow the order of operations (PEMDAS/BODMAS).
Evaluating Exponents First, we evaluate the exponents:
8 2 = 8 × 8 = 64
2 3 = 2 × 2 × 2 = 8
Substituting Values Now we substitute these values back into the expression:
6 + 64 ÷ 4 ⋅ 8
Performing Division and Multiplication Next, we perform the division and multiplication from left to right:
64 ÷ 4 = 16
16 ⋅ 8 = 128
Performing Addition Finally, we perform the addition:
6 + 128 = 134
Final Answer Therefore, the simplified expression is 134.
Examples
Understanding the order of operations is crucial in many real-life scenarios, such as calculating expenses or determining the outcome of a scientific experiment. For instance, if you are calculating the total cost of items with discounts and taxes, you need to apply the operations in the correct order to get the accurate final cost. Similarly, in programming, the order of operations determines how expressions are evaluated, which can affect the program's output. Correctly applying the order of operations ensures accurate and reliable results in various fields.
