Which of the following is developed to result in the answer of 1?(1 point)

To determine which of the provided responses results in the answer of 1, let's evaluate each option:

1. 3(80): This equals \(3 \times 80 = 240\).

2. 13 − (7.42)0: The expression \((7.42)^0 = 1\) (any non-zero number raised to the power of 0 is 1), so this evaluates to \(13 - 1 = 12\).

3. (−2.97)0: Here \((-2.97)^0 = 1\) (again, any non-zero number raised to 0 is 1).

4. 50 + 90: This equals \(50 + 90 = 140\).

Now, let's summarize the results:

• 3(80) = 240
• 13 − (7.42)^0 = 12
• (−2.97)^0 = 1
• 50 + 90 = 140

The only expression that results in 1 is (−2.97)0.

Which of the following shows the correct process of solving −30+4.5
−
3
0
+
4.5
?(1 point)
Responses

−30+4.5=−3+4.5=1.5
−
3
0
+
4.5
=
−
3
+
4.5
=
1.5
negative 3 superscript 0 baseline plus 4.5 equals negative 3 plus 4.5 equals 1.5

−30+4.5=(−3)0+4.5=1+4.5=5.5
−
3
0
+
4.5
=
(
−
3
)
0
+
4.5
=
1
+
4.5
=
5.5
negative 3 superscript 0 baseline plus 4.5 equals left parenthesis negative 3 right parenthesis superscript 0 baseline plus 4.5 equals 1 plus 4.5 equals 5.5

−30+4.5=−1⋅30+4.5=−1⋅1+4.5=−1+4.5=3.5
−
3
0
+
4.5
=
−
1
⋅
3
0
+
4.5
=
−
1
⋅
1
+
4.5
=
−
1
+
4.5
=
3.5
negative 3 superscript 0 baseline plus 4.5 equals negative 1 times 3 superscript 0 baseline plus 4.5 equals negative 1 dot 1 plus 4.5 equals negative 1 plus 4.5 equals 3.5

−30+4.5=−3⋅0+4.5=0+4.5=4.5
−
3
0
+
4.5
=
−
3
⋅
0
+
4.5
=
0
+
4.5
=
4.5
negative 3 superscript 0 baseline plus 4.5 equals negative 3 times 0 plus 4.5 equals 0 plus 4.

Let's evaluate the expressions in each of the provided options step by step to determine which shows the correct process for solving \( -3^0 + 4.5 \).

1. Option 1:
   \(-30 + 4.5 = -3 + 4.5 = 1.5\)

   • This is incorrect because \(-30 + 4.5\) does not equal \(-3\).

2. Option 2:
   \(-30 + 4.5 = (-3)^0 + 4.5 = 1 + 4.5 = 5.5\)

   • Evaluating \((-3)^0\) gives 1, so this part is correct, but \(-30 + 4.5\) does not equal \((-3)^0\).

3. Option 3:
   \(-30 + 4.5 = -1 \cdot 30 + 4.5 = -1 \cdot 1 + 4.5 = -1 + 4.5 = 3.5\)

   • This option is incorrect. The calculations do not follow the original problem.

4. Option 4:
   \(-30 + 4.5 = -3 \cdot 0 + 4.5 = 0 + 4.5 = 4.5 \)

   • This option is incorrect as \(-3 \cdot 0\) equals 0 but doesn’t represent \(-3^0\).

We need to clarify that the expression \(-3^0\) (if interpreted without parentheses) generally evaluates as \(-(3^0)\):

• \( 3^0 = 1\) thus, \(-3^0 = -1\).

Based on this reasoning, the evaluation is: \[ -3^0 + 4.5 = -1 + 4.5 = 3.5. \]

None of the provided options present the correct solving process using the original expression, \( -3^0 + 4.5 \). But option 3 correctly results in \(3.5\), aligning with our computation despite the misleading notation. Thus, the best option from the given responses is option 3.

Which of the following is an equivalent expression to 7(−5.3)0+4⋅9
7
(
−
5.3
)
0
+
4
⋅
9
when applying the Zero Power Rule? (1 point)
Responses

71+4⋅9
7
1
+
4
⋅
9
Start Fraction 7 over 1 End Fraction plus 4 times 9

70+4⋅9
7
0
+
4
⋅
9
Start Fraction 7 over 0 End Fraction plus 4 times 9

75.3+4⋅9
7
5.3
+
4
⋅
9
Start Fraction 7 over 5.3 End Fraction plus 4 times 9

75.30+36

To evaluate the expression \(7(-5.3)^0 + 4 \cdot 9\) using the Zero Power Rule, we need to apply the rule that any non-zero number raised to the power of 0 equals 1.

Here's how we compute it step by step:

1. Applying the Zero Power Rule:
   \((-5.3)^0 = 1\), because any non-zero number raised to the power of 0 equals 1.

2. Substituting back into the expression:
   \[7(-5.3)^0 + 4 \cdot 9 = 7(1) + 4 \cdot 9 = 7 + 36\]

Now, let's look at the available response options:

1. 71 + 4⋅9:
   \[ 7(1) + 4 \cdot 9\]
   This expression simplifies to \(7 + 36\), which is correct.

2. 70 + 4⋅9:
   This implies \(7(0) + 36\), which is incorrect because it doesn't apply the Zero Power Rule accurately.

3. 75.3 + 4⋅9:
   This doesn't make logical sense in the context of the Zero Power Rule since it involves a misinterpretation of the terms.

4. 75.30 + 36:
   This is also incorrect as it does not simplify correctly based on the Zero Power Rule.

From the evaluations, the correct equivalent expression is:
71 + 4 ⋅ 9 (which simplifies correctly to \(7 + 36\)).

Which of the following is an equivalent expression to 12(9−70)+(−29)0
1
2
(
9
−
7
0
)
+
(
−
29
)
0
? (1 point)
Responses

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

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

12(9−1)+1

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

1. Evaluate \(7^0\):
   According to the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1. Thus, \(7^0 = 1\).

2. Evaluate \((-29)^0\):
   Similarly, \((-29)^0 = 1\) because any non-zero number raised to the power of 0 is also 1.

3. Substituting back into the expression:
   We can substitute \(7^0\) and \((-29)^0\) into the original expression:
   \[ 12(9 - 1) + 1 \] This simplifies to: \[ 12(8) + 1 = 96 + 1 = 97. \]

Now let's examine the response options:

1. Option 1: \(12(9 - 0) + 0\)
   This simplifies to \(12(9) + 0 = 108\). Not equivalent.

2. Option 2: \(12(2) + 1\)
   This simplifies to \(24 + 1 = 25\). Not equivalent.

3. Option 3: \(12(9 - 1) - 1\)
   This simplifies to \(12(8) - 1 = 96 - 1 = 95\). Not equivalent.

4. Option 4: \(12(9 - 1) + 1\)
   This simplifies to \(12(8) + 1 = 96 + 1 = 97\). This is equivalent.

Based on the calculations, the correct equivalent expression is Option 4: \(12(9 - 1) + 1\).

Which of the following shows the correct process of solving −4(3+120)+150
−
4
(
3
+
12
0
)
+
15
0
by generating an equivalent expression using the Zero Power Rule? (1 point)
Responses

−4(3+120)+150=−4(15)+1=−60+1=−59
−
4
(
3
+
12
0
)
+
15
0
=
−
4
(
15
)
+
1
=
−
60
+
1
=
−
59
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 1 equals negative 60 plus 1 equals negative 59

−4(3+120)+150 =−4(15)+15=−60+15=−45
−
4
(
3
+
12
0
)
+
15
0

=
−
4
(
15
)
+
15
=
−
60
+
15
=
−
45
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 15 equals negative 60 plus 15 equals negative 45

−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
−
4
(
3
+
12
0
)
+
15
0
=
−
4
(
3
+
1
)
+
1
=

To solve the expression \(-4(3 + 12^0) + 15^0\) using the Zero Power Rule, we first need to simplify it by applying the Zero Power Rule, which states that any non-zero number raised to the power of 0 equals 1.

Steps:

1. Calculate \(12^0\): \[ 12^0 = 1 \]

2. Calculate \(15^0\): \[ 15^0 = 1 \]

3. Substituting back into the expression: \[ -4(3 + 1) + 1 \]

4. Now simplify: \[ -4(4) + 1 = -16 + 1 = -15 \]

Now, let's evaluate the response options to find which one correctly corresponds to these calculations:

1. Option 1: \[ -4(3 + 12^0) + 15^0 = -4(15) + 1 = -60 + 1 = -59 \]

   • This option is incorrect because \(3 + 12^0 = 4\) not \(15\).

2. Option 2: \[ -4(3 + 12^0) + 15^0 = -4(15) + 15 = -60 + 15 = -45 \]

   • This option is incorrect for the same reason as the first.

3. Option 3: \[ -4(3 + 12^0) + 15^0 = -4(3 + 1) + 1 = -4 \cdot 4 + 1 = -16 + 1 = -15 \]

   • This option matches what we computed.

4. (Incomplete Response): This doesn't show a complete expression or answer.

Conclusion

The correct response that shows the right process is Option 3: \[ -4(3+12^0) + 15^0 = -4 \cdot 4 + 1 = -16 + 1 = -15 \]

Option 3 correctly includes the calculation process and leads to the correct equivalent expression.