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Francesca tried to evaluate an expression. Here is her work:\newline3(5)218÷33(5)^2 - 18 \div 3\newline3(25)18÷3{Step 1}3(25) - 18 \div 3 \quad \{\text{Step 1}\}\newline7518÷3{Step 2}75 - 18 \div 3 \quad \{\text{Step 2}\}\newline57÷3{Step 3}57 \div 3 \quad \{\text{Step 3}\}\newline19{Step 4}19 \quad \{\text{Step 4}\}\newlineIs Francesca's work correct?\newline(A) No, Francesca made a mistake going from the given expression to Step 11. Francesca should have multiplied 33 and 55 before evaluating the exponent. The order of operations says to perform operations inside parentheses before you evaluate the exponent.\newline(B) No, Francesca made a mistake going from Step 22 to Step 33. Francesca should have divided 1818 by 33 before subtracting. The order of operations says to divide before you subtract.\newline(C) Yes, Francesca's work is correct.

Full solution

Q. Francesca tried to evaluate an expression. Here is her work:\newline3(5)218÷33(5)^2 - 18 \div 3\newline3(25)18÷3{Step 1}3(25) - 18 \div 3 \quad \{\text{Step 1}\}\newline7518÷3{Step 2}75 - 18 \div 3 \quad \{\text{Step 2}\}\newline57÷3{Step 3}57 \div 3 \quad \{\text{Step 3}\}\newline19{Step 4}19 \quad \{\text{Step 4}\}\newlineIs Francesca's work correct?\newline(A) No, Francesca made a mistake going from the given expression to Step 11. Francesca should have multiplied 33 and 55 before evaluating the exponent. The order of operations says to perform operations inside parentheses before you evaluate the exponent.\newline(B) No, Francesca made a mistake going from Step 22 to Step 33. Francesca should have divided 1818 by 33 before subtracting. The order of operations says to divide before you subtract.\newline(C) Yes, Francesca's work is correct.
  1. Evaluate Exponent: Francesca starts by evaluating the exponent in the expression 3(5)23(5)^2. She calculates 52=255^2 = 25. Then, she multiplies 33 by 2525 to get 7575. This is correct as per the order of operations (PEMDAS/BODMAS).
  2. Multiply Result: Next, Francesca calculates 18÷318 \div 3 in the expression 7518÷375 - 18 \div 3. She should have performed this division before subtracting from 7575. However, she subtracts first, getting 5757, and then divides 5757 by 33 to get 1919. This is incorrect because division should come before subtraction in the order of operations.

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