Question

Use the order of operations to evaluate this expression:

7 + (5 – 9)2 + 3(16 ÷ 8).


The value of the expression is
.

Answer 1

To evaluate the expression \( 7 + (5 - 9)2 + 3(16 \div 8) \), we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. Evaluate the expression inside the parentheses:
\[
5 - 9 = -4
\]

2. Replace the parentheses with the calculated value:
\[
7 + (-4)2 + 3(16 \div 8)
\]

3. Next, handle the exponent:
\[
(-4)2 = -4 \times -4 = 16
\]

4. Now, the expression becomes:
\[
7 + 16 + 3(16 \div 8)
\]

5. Next, evaluate the division:
\[
16 \div 8 = 2
\]

6. Replace the division result and evaluate the multiplication:
\[
3 \times 2 = 6
\]

7. Now, the expression is:
\[
7 + 16 + 6
\]

8. Finally, perform the addition from left to right:
\[
7 + 16 = 23
\]
\[
23 + 6 = 29
\]

The value of the expression is \( \boxed{29} \).