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