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Joey tried to evaluate an expression. Here is his work:\newline973+53÷25×2×3297 - 3 + 5^3 \div 25 \times 2 \times 3^2\newline973+125÷25×2×997 - 3 + 125 \div 25 \times 2 \times 9 {Step 11}\newline973+5×2×997 - 3 + 5 \times 2 \times 9 {Step 22}\newline973+10×997 - 3 + 10 \times 9 {Step 33}\newline973+9097 - 3 + 90 {Step 44}\newline979397 - 93 {Step 55}\newline44 {Step 66}\newlineIs Joey's work correct?\newline(A)No, Joey made a mistake going from the given expression to Step 11. Joey should have multiplied 22 and 33 instead of evaluating exponents. The order of operations says to multiply before you evaluate exponents.\newline(B)No, Joey made a mistake going from Step 44 to Step 55. Joey should have subtracted 33 from 973+125÷25×2×997 - 3 + 125 \div 25 \times 2 \times 900 before adding. The order of operations says to add and subtract from left to right.\newline(C)Yes, Joey's work is correct.

Full solution

Q. Joey tried to evaluate an expression. Here is his work:\newline973+53÷25×2×3297 - 3 + 5^3 \div 25 \times 2 \times 3^2\newline973+125÷25×2×997 - 3 + 125 \div 25 \times 2 \times 9 {Step 11}\newline973+5×2×997 - 3 + 5 \times 2 \times 9 {Step 22}\newline973+10×997 - 3 + 10 \times 9 {Step 33}\newline973+9097 - 3 + 90 {Step 44}\newline979397 - 93 {Step 55}\newline44 {Step 66}\newlineIs Joey's work correct?\newline(A)No, Joey made a mistake going from the given expression to Step 11. Joey should have multiplied 22 and 33 instead of evaluating exponents. The order of operations says to multiply before you evaluate exponents.\newline(B)No, Joey made a mistake going from Step 44 to Step 55. Joey should have subtracted 33 from 973+125÷25×2×997 - 3 + 125 \div 25 \times 2 \times 900 before adding. The order of operations says to add and subtract from left to right.\newline(C)Yes, Joey's work is correct.
  1. Evaluate Expression: Joey starts by evaluating the expression 973+53÷25×2×3297 - 3 + 5^3 \div 25 \times 2 \times 3^2. He calculates 535^3 as 125125 and 323^2 as 99.
  2. Calculate Exponents and Division: Joey then divides 125125 by 2525 to get 55, and continues with 5×2×95 \times 2 \times 9.
  3. Perform Multiplication: Joey multiplies 55 by 22 to get 1010, and then multiplies 1010 by 99 to get 9090.
  4. Complete Addition and Subtraction: Joey then adds 9090 to 9494 (97397 - 3). He should have subtracted 33 from 9797 first, then added 9090.

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