Simplify $3^2+3\left(6-2^2\right) \div 6$
A. 4
B. 10
C. 11
D. 7
Answer (2)
Evaluate the exponents: 3 2 = 9 and 2 2 = 4 .
Evaluate the parentheses: 6 − 4 = 2 .
Perform multiplication and division: 3 × 2 = 6 and 6 ÷ 6 = 1 .
Perform addition: 9 + 1 = 10 . The simplified expression is 10 .
Explanation
Understanding the expression We are asked to simplify the expression 3 2 + 3 ( 6 − 2 2 ) ÷ 6 . To do this, we will follow the order of operations (PEMDAS/BODMAS).
Evaluating exponents First, we evaluate the exponents: 3 2 = 9 and 2 2 = 4 . So the expression becomes 9 + 3 ( 6 − 4 ) ÷ 6 .
Evaluating parentheses Next, we evaluate the expression inside the parentheses: 6 − 4 = 2 . So the expression becomes 9 + 3 ( 2 ) ÷ 6 .
Performing multiplication Now, we perform the multiplication: 3 ( 2 ) = 6 . So the expression becomes 9 + 6 ÷ 6 .
Performing division Next, we perform the division: 6 ÷ 6 = 1 . So the expression becomes 9 + 1 .
Performing addition Finally, we perform the addition: 9 + 1 = 10 . Therefore, the simplified expression is 10 .
Examples
Understanding order of operations is crucial in many fields, such as computer programming, engineering, and finance. For example, when writing code, the order in which operations are performed can significantly affect the outcome of a calculation. In finance, accurately calculating returns on investments requires a precise understanding of the order of operations to ensure correct results. Consider calculating the future value of an investment with compound interest; the formula relies on the correct order to yield accurate predictions.
The simplified expression of 3 2 + 3 ( 6 − 2 2 ) ÷ 6 is 10 . Therefore, the correct answer is option B. This was derived through the order of operations step by step, starting from exponents to addition.
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