Question

nina tried to evaluate an expression. here is her work:
$(5\cdot 4 - 14 + 2)^2 + 16 \div 2$
$= (20 - 14 + 2)^2 + 16 \div 2$ step 1
$= (6 + 2)^2 + 16 \div 2$ step 2
$= 8^2 + 16 \div 2$ step 3
$= 64 + 16 \div 2$ step 4
$= 80 \div 2$ step 5
$= 40$ step 6
is ninas work correct?
no, nina made a mistake going from step 1 to step 2. nina should have squared 2 before subtracting. the order of operations says to evaluate exponents before you subtract.
no, nina made a mistake going from step 4 to step 5. nina should have divided 16 by 2 before adding. the order of operations says to divide before you add.
yes, ninas work is correct.

Explanation:

Step1: Recall order of operations (PEMDAS/BODMAS)

Operations order: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

Step2: Verify Step1 to Step4

Calculate inside parentheses: $5 \cdot 4 = 20$, $20 - 14 + 2 = 8$, $8^2 = 64$. Steps 1-4 are correct.

Step3: Check Step4 to Step5

Step4: $64 + 16 \div 2$. Division comes before addition: $16 \div 2 = 8$, then $64 + 8 = 72$. Nina incorrectly added first.

Answer:

No, Nina made a mistake going from Step 4 to Step 5. Nina should have divided 16 by 2 before adding. The order of operations says to divide before you add.