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

Question

? (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: \( \frac{1}{2}(9 - 1) + 1 \)