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

Question

Responses

1/2(9−1)+1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis plus 1

1/2(2)+1
Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1

1/2(9−0)+0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0

1/2(9−1)−1

Answer 1

Let's simplify the original expression step by step:

1. The expression is \( \frac{1}{2}(9−7^0)+(−29)^0 \).

2. First, calculate \( 7^0 \) and \( (-29)^0 \):

   • Any non-zero number raised to the power of 0 is 1, so \( 7^0 = 1 \) and \( (-29)^0 = 1 \).

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

4. Now simplify \( 9 - 1 = 8 \): \[ \frac{1}{2}(8) + 1 \]

5. Calculate \( \frac{1}{2}(8) = 4 \): \[ 4 + 1 = 5 \]

So the simplified version of the original expression is \( 5 \).

Now let's check each response to see which one is equivalent to the simplified expression.

1. \( \frac{1}{2}(9−1)+1 \):

   • \( 9 - 1 = 8 \), then \( \frac{1}{2}(8) + 1 = 4 + 1 = 5 \).
   • This is equivalent.

2. \( \frac{1}{2}(2)+1 \):

   • \( \frac{1}{2}(2) + 1 = 1 + 1 = 2 \).
   • This is not equivalent.

3. \( \frac{1}{2}(9−0)+0 \):

   • \( 9 - 0 = 9 \), then \( \frac{1}{2}(9) + 0 = 4.5 + 0 = 4.5 \).
   • This is not equivalent.

4. \( \frac{1}{2}(9−1)−1 \):

   • \( 9 - 1 = 8 \), then \( \frac{1}{2}(8) - 1 = 4 - 1 = 3 \).
   • This is not equivalent.

The only equivalent expression is:

\( \frac{1}{2}(9−1)+1 \).