Question

monica tried to evaluate an expression. here is her work:
$(7 + 9) - (2 \cdot 7 - 10) + 8 \div 2^2$
$= 16 - (14 - 10) + 8 \div 2^2$ step 1
$= 16 - 4 + 8 \div 2^2$ step 2
$= 16 - 4 + 8 \div 4$ step 3
$= 16 - 4 + 2$ step 4
$= 12 + 2$ step 5
$= 14$ step 6
is monicas work correct?
no, monica made a mistake going from step 1 to step 2. monica should still have included parentheses around 4 + 8. the order of operations says to perform all operations inside parentheses first.
no, monica made a mistake going from step 2 to step 3. monica should have divided 8 by 2 before evaluating the exponent. the order of operations says to divide before you evaluate exponents.
yes, monica’s work is correct.

Explanation:

Step1: Verify Step1-2

Calculate inside parentheses: $2\cdot7-10=14-10=4$. Monica's Step2 is correct.

Step2: Verify Step2-3

Evaluate exponent first: $2^2=4$. Monica's Step3 is correct.

Step3: Verify Step3-4

Perform division: $8\div4=2$. Monica's Step4 is correct.

Step4: Verify Step4-6

Do left-right addition/subtraction: $16-4=12$, $12+2=14$. Monica's steps are correct.

Step5: Evaluate all options

First two options claim errors that do not exist; the third option is accurate.

Answer:

Yes, Monica's work is correct.