Question

Which of the following is an equivalent expression to one over two and parentheses 9-7 super script 0+ and parentheses -29 superscript zero would it be 1/2 and parentheses nine minus one and then minus one or would it be 1/2 and parentheses 2+ one or would it be 1/2 and parentheses 9-0 and then +0 or 1/2 and parentheses nine minus one and then + one

Answer 1

To analyze the expression \( \frac{1}{2}(9 - 7^0) + (-29^0) \), we first simplify the components:

1. Evaluate \( 7^0 \): By the property of exponents, any non-zero number raised to the power of zero is 1. Thus, \( 7^0 = 1 \).

2. Now substitute this back into the expression:
\[
\frac{1}{2}(9 - 1) + (-29^0)
\]

3. Next, evaluate \( -29^0 \): Again, any non-zero number raised to the power of zero is 1, so \( -29^0 = -1 \).

4. Substituting back, we get:
\[
\frac{1}{2}(9 - 1) - 1
\]

5. Now simplify inside the parentheses:
\[
9 - 1 = 8
\]

6. So now we have:
\[
\frac{1}{2}(8) - 1
\]

7. Calculate \( \frac{1}{2}(8) = 4 \):
\[
4 - 1 = 3
\]

Now, let's look at the provided options and see which matches after performing similar operations:

1. **Option 1:** \( \frac{1}{2}(9 - 1) - 1 \) simplifies to:
\[
\frac{1}{2}(8) - 1 = 4 - 1 = 3
\]

2. **Option 2:** \( \frac{1}{2}(2 + 1) \) simplifies to:
\[
\frac{1}{2}(3) = 1.5
\]

3. **Option 3:** \( \frac{1}{2}(9 - 0) + 0 \) simplifies to:
\[
\frac{1}{2}(9) + 0 = 4.5
\]

4. **Option 4:** \( \frac{1}{2}(9 - 1) + 1 \) simplifies to:
\[
\frac{1}{2}(8) + 1 = 4 + 1 = 5
\]

The only option that results in 3 is **Option 1**:
\[
\frac{1}{2}(9 - 1) - 1
\]

Thus, the equivalent expression is **Option 1: \( \frac{1}{2}(9 - 1) - 1 \)**.