Which of the following is an equivalent expression to 12(9−7^0)+(−29)^0

Let's evaluate the expression \( 12(9 - 7^0) + (-29)^0 \).

1. First, we calculate \( 7^0 \) and \( (-29)^0 \):

   • Any non-zero number raised to the power of 0 equals 1, so:
     • \( 7^0 = 1 \)
     • \( (-29)^0 = 1 \)

2. Now substitute these values back into the expression: \[ 12(9 - 1) + 1 \]

3. Simplify the expression inside the parentheses: \[ 9 - 1 = 8 \]

4. Multiply: \[ 12 \times 8 = 96 \]

5. Finally, add: \[ 96 + 1 = 97 \]

Now, let's examine the answer choices given:

1. \( 12(2) + 1 \): Evaluates to \( 24 + 1 = 25 \) (not equivalent)
2. \( 12(9 - 0) + 0 \): Evaluates to \( 12 \times 9 + 0 = 108 + 0 = 108 \) (not equivalent)
3. \( 12(9 - 1) + 1 \): Evaluates to \( 12 \times 8 + 1 = 96 + 1 = 97 \) (this is equivalent)
4. \( 12(9 - 1) - 1 \): Evaluates to \( 12 \times 8 - 1 = 96 - 1 = 95 \) (not equivalent)

The equivalent expression to \( 12(9 - 7^0) + (-29)^0 \) is: \( 12(9 - 1) + 1 \).