Which of the following is an equivalent expression to 12(9−70)+(−29)0

To determine an equivalent expression to the given expression \(12(9 - 70) + (-29)0\), we can simplify it step by step.

1. First, recognize that anything multiplied by \(0\) is \(0\): \[ (-29)0 = 0 \] Thus, the expression simplifies to: \[ 12(9 - 70) + 0 \]

2. Now, we can further simplify \(12(9 - 70)\): \[ 9 - 70 = -61 \] Therefore: \[ 12(-61) + 0 = -732 + 0 = -732 \]

Now, we will examine each response option:

1. 12(9−0)+0:

   • This evaluates to \(12(9) + 0 = 108 + 0 = 108\), which is not equivalent to \(-732\).

2. Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0:

   • This evaluates to \(\frac{1}{2}(9) + 0 = \frac{9}{2} + 0 = 4.5\), which is not equivalent to \(-732\).

3. 12(9−1)−1:

   • This evaluates to \(12(8) - 1 = 96 - 1 = 95\), which is not equivalent to \(-732\).

4. Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1:

   • This evaluates to \(\frac{1}{2}(8) - 1 = 4 - 1 = 3\), which is not equivalent to \(-732\).

5. 12(2)+1:

   • This evaluates to \(12(2) + 1 = 24 + 1 = 25\), which is not equivalent to \(-732\).

6. 12(9−1)+1:

   • This evaluates to \(12(8) + 1 = 96 + 1 = 97\), which is not equivalent to \(-732\).

None of the response options provided are equivalent to the expression \(12(9 - 70) + (-29)0\), which simplifies to \(-732\). Thus, none are correct.