Question

question 6

evaluate the following expression using the order of operations.

(10 + 2 + (6 - 3)^3 + 2(4))

• 24
• 48
• 40
• 17

Explanation:

Evaluate parentheses

Using the Order of Operations knowledge point

$$ (6 - 3) = 3 $$

The expression becomes:

$$ 10 + 2 + 3^3 + 2(4) $$

Evaluate exponents

Using the Exponentiation Rules knowledge point

$$ 3^3 = 3 \times 3 \times 3 = 27 $$

The expression becomes:

$$ 10 + 2 + 27 + 2(4) $$

Perform multiplication

Using the Order of Operations knowledge point

$$ 2(4) = 8 $$

The expression becomes:

$$ 10 + 2 + 27 + 8 $$

Perform addition from left to right

Using the Order of Operations knowledge point

$$ 10 + 2 + 27 + 8 = 12 + 27 + 8 = 39 + 8 = 47 $$

Wait, let me re-read the expression from the image carefully.
Looking closely at the image:
The expression is:
\(10 \div 2 + (6 - 3)^3 + 2(4)\)
Ah! The symbol between 10 and 2 is a division sign (\(\div\)), not a plus sign (\(+\)).
Let's re-evaluate with division:

$$ 10 \div 2 + (6 - 3)^3 + 2(4) $$

Evaluate parentheses

Using the Order of Operations knowledge point

$$ (6 - 3) = 3 $$

The expression becomes:

$$ 10 \div 2 + 3^3 + 2(4) $$

Evaluate exponents

Using the Exponentiation Rules knowledge point

$$ 3^3 = 27 $$

The expression becomes:

$$ 10 \div 2 + 27 + 2(4) $$

Perform division and multiplication from left to right

Using the Order of Operations knowledge point

$$ 10 \div 2 = 5 $$

$$ 2(4) = 8 $$

The expression becomes:

$$ 5 + 27 + 8 $$

Perform addition

Using the Order of Operations knowledge point

$$ 5 + 27 + 8 = 32 + 8 = 40 $$

Answer:

• (A) 24
• (B) 48
• (C) 40 (Correct answer)
• (D) 17