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

\( 12(2) + 1 \): Evaluates to \( 24 + 1 = 25 \) (not equivalent)
\( 12(9 - 0) + 0 \): Evaluates to \( 12 \times 9 + 0 = 108 + 0 = 108 \) (not equivalent)
\( 12(9 - 1) + 1 \): Evaluates to \( 12 \times 8 + 1 = 96 + 1 = 97 \) (this is equivalent)
\( 12(9 - 1) - 1 \): Evaluates to \( 12 \times 8 - 1 = 96 - 1 = 95 \) (not equivalent)

Question

Which of the following is an equivalent expression to 12(9−7^0)+(−29)^0
1
2
(
9
−
7
0
)
+
(
−
29
)
0
? (1 point)
Responses

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

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

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

12(9−1)−1

GPT-4o mini · Answer

Let's evaluate the expression $ 12(9 - 7^0) + (-29)^0 $. 1. First, we calculate $ 7^0 $ and $ (-29)^0 $: - Any non-zero number raised to the power of 0 equals 1, so: - $ 7^0 = 1 $ - $ (-29)^0 = 1 $ 2. Now substitute these values back into the expression: $$ 12(9 - 1) + 1 $$ 3. Simplify the expression inside the parentheses: $$ 9 - 1 = 8 $$ 4. Multiply: $$ 12 \times 8 = 96 $$ 5. Finally, add: $$ 96 + 1 = 97 $$ Now, let's examine the answer choices given: 1. **$ 12(2) + 1 $**: Evaluates to $ 24 + 1 = 25 $ (not equivalent) 2. **$ 12(9 - 0) + 0 $**: Evaluates to $ 12 \times 9 + 0 = 108 + 0 = 108 $ (not equivalent) 3. **$ 12(9 - 1) + 1 $**: Evaluates to $ 12 \times 8 + 1 = 96 + 1 = 97 $ (this is equivalent) 4. **$ 12(9 - 1) - 1 $**: Evaluates to $ 12 \times 8 - 1 = 96 - 1 = 95 $ (not equivalent) The equivalent expression to $ 12(9 - 7^0) + (-29)^0 $ is: **$ 12(9 - 1) + 1 $**.