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

Question

? (1 point)
Responses

1/2(2)+1
Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1

1/2(9−0)+0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0

1/2(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1

1/2(9−1)+1

Answer 1

First, let's simplify the original expression \( 12(9 - 7^0) + (-29)^0 \).

We know that any number to the power of 0 is 1 (except for 0 itself). Thus,

\[ 7^0 = 1 \quad \text{and} \quad (-29)^0 = 1 \]

Substituting these values into the expression, we get:

\[ 12(9 - 1) + 1 \]

Now, simplify \( 9 - 1 \):

\[ 12(8) + 1 = 96 + 1 = 97 \]

Now let's evaluate each of the provided answer choices to see if any simplify to 97.

1. Choice 1: \( \frac{1}{2}(2) + 1 \)

   \[ = 1 + 1 = 2 \]

2. Choice 2: \( \frac{1}{2}(9 - 0) + 0 \)

   \[ = \frac{1}{2}(9) + 0 = \frac{9}{2} + 0 = 4.5 \]

3. Choice 3: \( \frac{1}{2}(9 - 1) - 1 \)

   \[ = \frac{1}{2}(8) - 1 = 4 - 1 = 3 \]

4. Choice 4: \( \frac{1}{2}(9 - 1) + 1 \)

   \[ = \frac{1}{2}(8) + 1 = 4 + 1 = 5 \]

None of the choices evaluate to \( 97 \). However, by breaking down the expressions into simpler forms, we can see that none are equivalent to the original expression provided in the question.

Thus, the answer is that none of the provided options are equivalent to the expression \( 12(9 - 7^0) + (-29)^0 \).