Question
Which of the following is an equivalent expression to 7(−5.3)0+4⋅9 when applying the Zero Power Rule? (1 point).
Responses
71+4⋅9
Start Fraction 7 over 1 End Fraction plus 4 times 9
70+4⋅9
Start Fraction 7 over 0 End Fraction plus 4 times 9
75.3+4⋅9
Start Fraction 7 over 5.3 End Fraction plus 4 times 9
75.30+36
Responses
71+4⋅9
Start Fraction 7 over 1 End Fraction plus 4 times 9
70+4⋅9
Start Fraction 7 over 0 End Fraction plus 4 times 9
75.3+4⋅9
Start Fraction 7 over 5.3 End Fraction plus 4 times 9
75.30+36
Answers
Answer
Which of the following is an equivalent expression to 12(9−70)+(−29)0 ? (1 point)
Responses
12(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1
12(9−1)+1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 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(2)+1
Responses
12(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1
12(9−1)+1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 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(2)+1
Answer
so what's the answer???
Answer
(1 point)
Responses
A. 12(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1
B. 12(9−1)+1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis plus 1
C. 12(9−0)+0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0
D. 12(2)+1
Responses
A. 12(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1
B. 12(9−1)+1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis plus 1
C. 12(9−0)+0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0
D. 12(2)+1
Answer
can u just pick one and pick the right one ty
Answer
go back and check and see if this is right
Answered by
GPT-4o mini
To apply the Zero Power Rule, we need to evaluate the expression \(7(−5.3)^0 + 4 \cdot 9\).
The Zero Power Rule states that any non-zero number raised to the power of zero is equal to 1. Thus, we can simplify \( (−5.3)^0 \) as follows:
\[
(−5.3)^0 = 1
\]
Now substituting this back into the expression:
\[
7(−5.3)^0 + 4 \cdot 9 = 7(1) + 4 \cdot 9
\]
This simplifies to:
\[
7 + 4 \cdot 9
\]
Next, calculate \(4 \cdot 9\):
\[
4 \cdot 9 = 36
\]
Now, we can rewrite the expression:
\[
7 + 36
\]
So, combining these gives:
\[
7 + 36 = 43
\]
Now let's look at the provided responses. Among those listed, the equivalent expression after applying the Zero Power Rule and simplifying is:
**75.30 + 36**, which is simply \(7 + 36\).
Therefore, the correct answer is:
**75.30 + 36**.
The Zero Power Rule states that any non-zero number raised to the power of zero is equal to 1. Thus, we can simplify \( (−5.3)^0 \) as follows:
\[
(−5.3)^0 = 1
\]
Now substituting this back into the expression:
\[
7(−5.3)^0 + 4 \cdot 9 = 7(1) + 4 \cdot 9
\]
This simplifies to:
\[
7 + 4 \cdot 9
\]
Next, calculate \(4 \cdot 9\):
\[
4 \cdot 9 = 36
\]
Now, we can rewrite the expression:
\[
7 + 36
\]
So, combining these gives:
\[
7 + 36 = 43
\]
Now let's look at the provided responses. Among those listed, the equivalent expression after applying the Zero Power Rule and simplifying is:
**75.30 + 36**, which is simply \(7 + 36\).
Therefore, the correct answer is:
**75.30 + 36**.
Answered by
GPT-4o mini
To simplify the expression \( 12(9 - 70) + (-29)^0 \), we start by evaluating each part.
1. **Evaluate \((-29)^0\)**:
According to the Zero Power Rule, any non-zero number raised to the power of zero is equal to 1.
Thus, \((-29)^0 = 1\).
2. **Evaluate \( (9 - 70) \)**:
\[
9 - 70 = -61
\]
3. **Substitute these back into the original expression**:
\[
12(9 - 70) + (-29)^0 = 12(-61) + 1
\]
Now calculate \( 12(-61) \):
\[
12(-61) = -732
\]
Therefore, the expression simplifies to:
\[
-732 + 1 = -731
\]
Now, let’s examine the provided response options to see which one is equivalent to \(-731\):
1. **12(9 - 1) - 1**:
\[
12(8) - 1 = 96 - 1 = 95
\]
2. **12(9 - 1) + 1**:
\[
12(8) + 1 = 96 + 1 = 97
\]
3. **12(9 - 0) + 0**:
\[
12(9) + 0 = 108 + 0 = 108
\]
4. **12(2) + 1**:
\[
12(2) + 1 = 24 + 1 = 25
\]
None of these calculations yield \(-731\). It seems that none of the options provided is equivalent to the simplified expression.
Could you please check if there's an oversight in the expression or the options provided?
1. **Evaluate \((-29)^0\)**:
According to the Zero Power Rule, any non-zero number raised to the power of zero is equal to 1.
Thus, \((-29)^0 = 1\).
2. **Evaluate \( (9 - 70) \)**:
\[
9 - 70 = -61
\]
3. **Substitute these back into the original expression**:
\[
12(9 - 70) + (-29)^0 = 12(-61) + 1
\]
Now calculate \( 12(-61) \):
\[
12(-61) = -732
\]
Therefore, the expression simplifies to:
\[
-732 + 1 = -731
\]
Now, let’s examine the provided response options to see which one is equivalent to \(-731\):
1. **12(9 - 1) - 1**:
\[
12(8) - 1 = 96 - 1 = 95
\]
2. **12(9 - 1) + 1**:
\[
12(8) + 1 = 96 + 1 = 97
\]
3. **12(9 - 0) + 0**:
\[
12(9) + 0 = 108 + 0 = 108
\]
4. **12(2) + 1**:
\[
12(2) + 1 = 24 + 1 = 25
\]
None of these calculations yield \(-731\). It seems that none of the options provided is equivalent to the simplified expression.
Could you please check if there's an oversight in the expression or the options provided?
Answered by
GPT-4o mini
Apologies for the confusion in my previous response. Let's clarify the result step-by-step and check the options again.
The expression we started with is:
\[
12(9 - 70) + (-29)^0
\]
Let's simplify this again:
1. **Evaluate \((-29)^0\)**:
- \((-29)^0 = 1\)
2. **Evaluate \( (9 - 70) \)**:
- \(9 - 70 = -61\)
3. **Then substitute back into the expression**:
- \(12(9 - 70) + (-29)^0 = 12(-61) + 1\)
4. **Calculate \(12(-61)\)**:
- \(12 \times -61 = -732\)
5. **Combine results**:
- \(-732 + 1 = -731\)
Now, we need to check which of the provided options is equivalent to \(-731\):
Let's evaluate each option again:
1. **Option 1: \(12(9 - 1) - 1\)**:
- \(12(8) - 1 = 96 - 1 = 95\)
2. **Option 2: \(12(9 - 1) + 1\)**:
- \(12(8) + 1 = 96 + 1 = 97\)
3. **Option 3: \(12(9 - 0) + 0\)**:
- \(12(9) + 0 = 108 + 0 = 108\)
4. **Option 4: \(12(2) + 1\)**:
- \(12(2) + 1 = 24 + 1 = 25\)
None of the provided options match \(-731\). Therefore, it seems there may be a misalignment in the question or the options given.
No options are equivalent to the simplified result of \(-731\).
If possible, can you please verify the expression or the response options again?
The expression we started with is:
\[
12(9 - 70) + (-29)^0
\]
Let's simplify this again:
1. **Evaluate \((-29)^0\)**:
- \((-29)^0 = 1\)
2. **Evaluate \( (9 - 70) \)**:
- \(9 - 70 = -61\)
3. **Then substitute back into the expression**:
- \(12(9 - 70) + (-29)^0 = 12(-61) + 1\)
4. **Calculate \(12(-61)\)**:
- \(12 \times -61 = -732\)
5. **Combine results**:
- \(-732 + 1 = -731\)
Now, we need to check which of the provided options is equivalent to \(-731\):
Let's evaluate each option again:
1. **Option 1: \(12(9 - 1) - 1\)**:
- \(12(8) - 1 = 96 - 1 = 95\)
2. **Option 2: \(12(9 - 1) + 1\)**:
- \(12(8) + 1 = 96 + 1 = 97\)
3. **Option 3: \(12(9 - 0) + 0\)**:
- \(12(9) + 0 = 108 + 0 = 108\)
4. **Option 4: \(12(2) + 1\)**:
- \(12(2) + 1 = 24 + 1 = 25\)
None of the provided options match \(-731\). Therefore, it seems there may be a misalignment in the question or the options given.
No options are equivalent to the simplified result of \(-731\).
If possible, can you please verify the expression or the response options again?
Answered by
GPT-4o mini
Thanks for your patience. Let's analyze the original expression and the given response options again to find an equivalent expression.
The original expression is:
\[
12(9 - 70) + (-29)^0
\]
### Step-by-Step Evaluation:
1. **Calculate \((-29)^0\)**:
- \((-29)^0 = 1\)
2. **Calculate \(9 - 70\)**:
- \(9 - 70 = -61\)
3. **Evaluate the entire expression**:
\[
12(9 - 70) + (-29)^0 = 12(-61) + 1
\]
4. **Calculate \(12 \times (-61)\)**:
- \(12 \times (-61) = -732\)
5. **Combine results**:
\[
-732 + 1 = -731
\]
### Now, let's analyze the response options:
**A. \(12(9 - 1) - 1\)**:
\[
12(8) - 1 = 96 - 1 = 95
\]
**B. \(12(9 - 1) + 1\)**:
\[
12(8) + 1 = 96 + 1 = 97
\]
**C. \(12(9 - 0) + 0\)**:
\[
12(9) + 0 = 108 + 0 = 108
\]
**D. \(12(2) + 1\)**:
\[
12(2) + 1 = 24 + 1 = 25
\]
### Conclusion
None of the options A, B, C, or D results in \(-731\). If your original expression and the options are correct, then none match the calculated value.
However, if you consider the final output, \(-731\) cannot be matched with the responses provided.
If there was a misunderstanding regarding the original expression, please confirm it for further clarification. If everything is accurate, the answer must be none of the options.
The original expression is:
\[
12(9 - 70) + (-29)^0
\]
### Step-by-Step Evaluation:
1. **Calculate \((-29)^0\)**:
- \((-29)^0 = 1\)
2. **Calculate \(9 - 70\)**:
- \(9 - 70 = -61\)
3. **Evaluate the entire expression**:
\[
12(9 - 70) + (-29)^0 = 12(-61) + 1
\]
4. **Calculate \(12 \times (-61)\)**:
- \(12 \times (-61) = -732\)
5. **Combine results**:
\[
-732 + 1 = -731
\]
### Now, let's analyze the response options:
**A. \(12(9 - 1) - 1\)**:
\[
12(8) - 1 = 96 - 1 = 95
\]
**B. \(12(9 - 1) + 1\)**:
\[
12(8) + 1 = 96 + 1 = 97
\]
**C. \(12(9 - 0) + 0\)**:
\[
12(9) + 0 = 108 + 0 = 108
\]
**D. \(12(2) + 1\)**:
\[
12(2) + 1 = 24 + 1 = 25
\]
### Conclusion
None of the options A, B, C, or D results in \(-731\). If your original expression and the options are correct, then none match the calculated value.
However, if you consider the final output, \(-731\) cannot be matched with the responses provided.
If there was a misunderstanding regarding the original expression, please confirm it for further clarification. If everything is accurate, the answer must be none of the options.
Answered by
GPT-4o mini
I apologize for the confusion earlier. Based on the original expression and its value, none of the options match \(-731\). However, if I am to select the closest option based on the structure given, I would choose option **B**:
**B.** \(12(9 - 1) + 1\)
While it does not equal \(-731\), it is formatted similarly to the original expression.
If you meant for me to simply pick one option, **B** is my selection. Thank you for your understanding!
**B.** \(12(9 - 1) + 1\)
While it does not equal \(-731\), it is formatted similarly to the original expression.
If you meant for me to simply pick one option, **B** is my selection. Thank you for your understanding!
Answered by
GPT-4o mini
Let’s go through the problem step by step carefully again.
### Original Expression:
\[
12(9 - 70) + (-29)^0
\]
### Evaluating the components:
1. **Calculate \((-29)^0\)**:
\[
(-29)^0 = 1 \quad \text{(since any non-zero number to the power of 0 is 1)}
\]
2. **Calculate \(9 - 70\)**:
\[
9 - 70 = -61
\]
3. **Substituting back into the original expression**:
\[
12(9 - 70) + 1 = 12(-61) + 1
\]
4. **Calculate \(12 \times -61\)**:
\[
12 \times -61 = -732
\]
5. **Combine the results**:
\[
-732 + 1 = -731
\]
### Simplifying the Options:
Now let's re-evaluate the options to find one that matches or is equivalent to the original expression:
1. **Option A: \(12(9 - 1) - 1\)**:
\[
12(8) - 1 = 96 - 1 = 95
\]
2. **Option B: \(12(9 - 1) + 1\)**:
\[
12(8) + 1 = 96 + 1 = 97
\]
3. **Option C: \(12(9 - 0) + 0\)**:
\[
12(9) + 0 = 108 + 0 = 108
\]
4. **Option D: \(12(2) + 1\)**:
\[
12(2) + 1 = 24 + 1 = 25
\]
### Summary:
To summarize:
- The original expression evaluates to \(-731\).
- All options simplify to positive values and do not equal \(-731\).
### Conclusion:
**None of the provided options are equivalent to the original expression.** However, if you need to choose one, please go with:
**A. \(12(9 - 1) - 1\)** (as it's the only option that includes a subtraction).
If this was not the information you were seeking, please let me know how I can assist further!
### Original Expression:
\[
12(9 - 70) + (-29)^0
\]
### Evaluating the components:
1. **Calculate \((-29)^0\)**:
\[
(-29)^0 = 1 \quad \text{(since any non-zero number to the power of 0 is 1)}
\]
2. **Calculate \(9 - 70\)**:
\[
9 - 70 = -61
\]
3. **Substituting back into the original expression**:
\[
12(9 - 70) + 1 = 12(-61) + 1
\]
4. **Calculate \(12 \times -61\)**:
\[
12 \times -61 = -732
\]
5. **Combine the results**:
\[
-732 + 1 = -731
\]
### Simplifying the Options:
Now let's re-evaluate the options to find one that matches or is equivalent to the original expression:
1. **Option A: \(12(9 - 1) - 1\)**:
\[
12(8) - 1 = 96 - 1 = 95
\]
2. **Option B: \(12(9 - 1) + 1\)**:
\[
12(8) + 1 = 96 + 1 = 97
\]
3. **Option C: \(12(9 - 0) + 0\)**:
\[
12(9) + 0 = 108 + 0 = 108
\]
4. **Option D: \(12(2) + 1\)**:
\[
12(2) + 1 = 24 + 1 = 25
\]
### Summary:
To summarize:
- The original expression evaluates to \(-731\).
- All options simplify to positive values and do not equal \(-731\).
### Conclusion:
**None of the provided options are equivalent to the original expression.** However, if you need to choose one, please go with:
**A. \(12(9 - 1) - 1\)** (as it's the only option that includes a subtraction).
If this was not the information you were seeking, please let me know how I can assist further!
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