Question

Nina tried to evaluate an expression. Here is her work:
(54–14+2)2+16÷2
=
(20–14+2)2+16÷2 Step 1
=
(6+2)2+16÷2 Step 2
=
82+16÷2 Step 3
=
64+16÷2 Step 4
=
80÷2 Step 5
=
40 Step 6
Is Nina's work correct?




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Answer 1

Let's evaluate the expression step by step to see if Nina's work is correct:

The original expression is:
\((54 - 14 + 2)^2 + 16 \div 2\)

### Following the order of operations (PEMDAS/BODMAS):

1. **Parentheses/Brackets**: First, solve inside the parentheses.
\[
54 - 14 + 2 = 40 + 2 = 42
\]
So, we now have:
\[
(42)^2 + 16 \div 2
\]

2. **Exponents/Orders**: Next, we square the result.
\[
42^2 = 1764
\]
So now, we have:
\[
1764 + 16 \div 2
\]

3. **Division**: Now, perform the division.
\[
16 \div 2 = 8
\]
So we have:
\[
1764 + 8
\]

4. **Addition**: Finally, perform the addition.
\[
1764 + 8 = 1772
\]

So, the final result of the expression \((54 - 14 + 2)^2 + 16 \div 2\) is **1772**.

### Now let's analyze Nina's steps:
1. **Step 1**: \( (54 - 14 + 2) \) correctly simplified to \( (20 - 14 + 2) \) should have been \( (42) \) instead.
2. The other steps continue from there with incorrect calculations based on the wrong parentheses evaluation.
3. Finally, she obtained 40 as the final result instead of 1772.

### Conclusion:
Nina's work is **not correct**. The correct answer to the expression is 1772.