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Simplify: 32×3−15−2×20

Adam wrote: 3−2×522

Nick wrote: 3×52

Shane wrote: 3−352

Who was correct and why?

(1 point)
Responses

Shane is correct because all that needs to be done is to make the negative exponents positive.
Shane is correct because all that needs to be done is to make the negative exponents positive.

None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.
None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.

Adam is correct because the negative exponent combines with the base and the denominator moves to the numerator.
Adam is correct because the negative exponent combines with the base and the denominator moves to the numerator.

Nick is correct because the negative exponent in the numerator can combine with the like base and the denominator negative exponent goes to the numerator.

1 answer

First, let's simplify the original expression \(32 \times 3 - 15 - 2 \times 20\):

  1. Calculate \(32 \times 3 = 96\).
  2. Calculate \(2 \times 20 = 40\).
  3. Substitute these values back into the expression: \[96 - 15 - 40\].
  4. Subtract \(15\) from \(96\): \[96 - 15 = 81\].
  5. Then subtract \(40\): \[81 - 40 = 41\].

Thus, the simplified expression is \(41\).

Now, let's examine each person's response:

  1. Adam wrote: \(3 - 2 \times 522\)
  2. Nick wrote: \(3 \times 52\)
  3. Shane wrote: \(3 - 352\)

Based on the calculations, none of the responses provided (Adam, Nick, or Shane) correctly simplified the original expression.

Let’s assess their correctness according to the provided potential responses:

  1. Shane's Explanation: Not applicable because the negative exponent concept doesn’t apply to this expression and is inconsistent with his result.
  2. None of these are correct: This response fits because each student produced an incorrect formula and didn't accurately represent the original mathematical operation.
  3. Adam's Explanation: This doesn't apply; the negative exponent scope isn't correctly utilized.
  4. Nick's Explanation: This also does not apply; again, the operation doesn't lead to a valid conclusion.

Since none of the responses correctly captured the simplification of the original expression, the suitable answer would be:

None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.

This option is correct overall, highlighting that each student misinterpreted the expression or the process for exponents.