Question

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

1/2(9−0)+0


1/2(9−1)−1

1/2(2)+1

1/2(9−1)+1

Answer 1

To simplify the expression \( \frac{1}{2}(9 - 7^0) + (-29)^0 \), let's break it down step by step:

1. Calculate \( 7^0 \):
- Any non-zero number raised to the power of 0 is 1.
- So, \( 7^0 = 1 \).

2. Calculate \( (-29)^0 \):
- The same rule applies; any non-zero number raised to the power of 0 is 1.
- Thus, \( (-29)^0 = 1 \).

Now substitute these values back into the original expression:

\[
\frac{1}{2}(9 - 1) + 1
\]

Simplify \( 9 - 1 \):

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

Next, calculate \( \frac{1}{2}(8) \):

\[
4 + 1 = 5
\]

Now, we want to find an equivalent expression from the given options.

Let's evaluate each option:

1. **Option 1**: \( \frac{1}{2}(9 - 0) + 0 \)
- This simplifies to \( \frac{1}{2}(9) + 0 = 4.5 + 0 = 4.5 \) (not equivalent).

2. **Option 2**: \( \frac{1}{2}(9 - 1) - 1 \)
- This simplifies to \( \frac{1}{2}(8) - 1 = 4 - 1 = 3 \) (not equivalent).

3. **Option 3**: \( \frac{1}{2}(2) + 1 \)
- This simplifies to \( 1 + 1 = 2 \) (not equivalent).

4. **Option 4**: \( \frac{1}{2}(9 - 1) + 1 \)
- This simplifies to \( \frac{1}{2}(8) + 1 = 4 + 1 = 5 \) (this is equivalent).

The correct choice is:

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