Which of the following is an equivalent expression to 12(9−7^0)+(−29)^0 ? (1 point)

Question

Responses

12(9−1)+1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis plus 1

12(2)+1
Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1

12(9−0)+0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0

12(9−1)−1

Answer 1

To find an equivalent expression to \( 12(9 - 7^0) + (-29)^0 \), we first need to simplify the original expression step by step.

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

2. Substitute \( 7^0 \) into the expression: \[ 12(9 - 1) + (-29)^0 \]

3. Calculate \( (-29)^0 \): \[ (-29)^0 = 1 \]

4. Substitute \( (-29)^0 \) into the expression: \[ 12(9 - 1) + 1 \]

5. Now simplify \( 9 - 1 \) and then \( 12(8) + 1 \): \[ 12(8) + 1 = 96 + 1 = 97 \]

Now, let's check the options given:

1. Option 1: \( 12(9−1)+1 \)
   This simplifies to:
   \( 12(8) + 1 = 96 + 1 = 97 \) (This is equivalent)

2. Option 2: \( \frac{1}{2}(9 - 1) + 1 \)
   Simplifying:
   \( \frac{1}{2}(8) + 1 = 4 + 1 = 5 \) (This is not equivalent)

3. Option 3: \( 12(9−0)+0 \)
   This simplifies to:
   \( 12(9) + 0 = 108 + 0 = 108 \) (This is not equivalent)

4. Option 4: \( 12(9−1)−1 \)
   This simplifies to:
   \( 12(8) - 1 = 96 - 1 = 95 \) (This is not equivalent)

Based on this, the only equivalent expression to the original is:

Option 1: \( 12(9−1)+1 \)