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

Question

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

Answer 1

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: $12(9-1)+1$.