Question

joey tried to evaluate an expression. here is his work:
$97 - 3 + 5^3 \div 25 \cdot 2 \cdot 3^2$
$= 97 - 3 + 125 \div 25 \cdot 2 \cdot 9$ step 1
$= 97 - 3 + 5 \cdot 2 \cdot 9$ step 2
$= 97 - 3 + 10 \cdot 9$ step 3
$= 97 - 3 + 90$ step 4
$= 97 - 93$ step 5
$= 4$ step 6
is joeys work correct?
no, joey made a mistake going from the given expression to step 1. joey should have multiplied 2 and 3 instead of evaluating exponents. the order of operations says to multiply before you evaluate exponents.
no, joey made a mistake going from step 4 to step 5. joey should have subtracted 3 from 97 before adding. the order of operations says to add and subtract from left to right.
yes, joeys work is correct.

Explanation:

Step1: Verify Step1 exponents

$5^3=125$, $3^2=9$, so Step1 is correct: $97 - 3 + 125 \div 25 \cdot 2 \cdot 9$

Step2: Verify Step2 division

$125\div25=5$, so Step2 is correct: $97 - 3 + 5 \cdot 2 \cdot 9$

Step3: Verify Step3 multiplication

$5\cdot2=10$, so Step3 is correct: $97 - 3 + 10 \cdot 9$

Step4: Verify Step4 multiplication

$10\cdot9=90$, so Step4 is correct: $97 - 3 + 90$

Step5: Check Step5 order error

Add/subtract left to right: $97-3=94$, then $94+90=184$. Joey incorrectly did $3+90=93$ first.

Answer:

No, Joey made a mistake going from Step 4 to Step 5. Joey should have subtracted 3 from 97 before adding. The order of operations says to add and subtract from left to right.