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

Question

Responses:

1 over 2(2) + 1

1 over 2(9 − 1) − 1

1 over 2(9 − 0) + 0

1 over 2(9 − 1) + 1

Answer 1

Let's simplify the expression \( \frac{1}{2}(9 - 7^0) + (-29)^0 \) step by step.

1. Calculate \( 7^0 \): \[ 7^0 = 1 \]

2. Next, calculate \( (-29)^0 \): \[ (-29)^0 = 1 \]

3. Now substitute these values back into the expression: \[ \frac{1}{2}(9 - 1) + 1 \]

4. Simplify inside the parentheses: \[ 9 - 1 = 8 \]

5. Now, plug it back in: \[ \frac{1}{2} \times 8 + 1 \]

6. Calculate \( \frac{1}{2} \times 8 \): \[ \frac{1}{2} \times 8 = 4 \]

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

Now, let's compare it to the choices provided:

1. \( \frac{1}{2}(2) + 1 \): \[ \frac{1}{2}(2) = 1 \quad \text{and} \quad 1 + 1 = 2 \]

2. \( \frac{1}{2}(9 - 1) - 1 \): \[ \frac{1}{2}(8) - 1 \quad \Rightarrow \quad 4 - 1 = 3 \]

3. \( \frac{1}{2}(9 - 0) + 0 \): \[ \frac{1}{2}(9) + 0 \quad \Rightarrow \quad \frac{9}{2} = 4.5 \]

4. \( \frac{1}{2}(9 - 1) + 1 \): \[ \frac{1}{2}(8) + 1 \quad \Rightarrow \quad 4 + 1 = 5 \]

The only expression that is equivalent to the original expression is:

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