Which of the following is an equivalent expression to 1/2(9−7 to the power of 0)+(−29)0

To simplify the original expression \( \frac{1}{2}(9 - 7^0) + (-29)^0 \), we can evaluate each part step-by-step.

1. First, we calculate \( 7^0 \): \[ 7^0 = 1 \]

2. Next, we substitute \( 7^0 \) back into the expression: \[ \frac{1}{2}(9 - 1) + (-29)^0 \]

3. Now, we calculate \( (-29)^0 \): \[ (-29)^0 = 1 \]

4. So far, we have: \[ \frac{1}{2}(9 - 1) + 1 \]

5. Now, we simplify further: \[ 9 - 1 = 8 \] Therefore, we have: \[ \frac{1}{2}(8) + 1 \]

6. Now we calculate \( \frac{1}{2}(8) \): \[ \frac{1}{2}(8) = 4 \]

7. Finally, we add the 1: \[ 4 + 1 = 5 \]

Now that we know the original expression simplifies to \( 5 \), we can check which of the provided options also equals \( 5 \):

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

   • Simplifies to \( \frac{1}{2}(9) + 0 = 4.5 + 0 = 4.5 \) (not equal to 5)

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

   • Simplifies to \( \frac{1}{2}(8) - 1 = 4 - 1 = 3 \) (not equal to 5)

3. Option: \( \frac{1}{2}(2) + 1 \)

   • Simplifies to \( \frac{1}{2}(2) + 1 = 1 + 1 = 2 \) (not equal to 5)

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

   • Simplifies to \( \frac{1}{2}(8) + 1 = 4 + 1 = 5 \) (this is equal to 5)

Based on the evaluation above, the equivalent expression is: \( \frac{1}{2}(9 - 1) + 1 \).