Question
Apply the Zero Power Rule to create an equivalent expression to (−40)^0 + 1/2(11−320) (−40)^0 + 1/2(11−320) = 1 +12 (2 − 3 )
Answers
Answer
no the right answers are 1,11 and 1
Answered by
GPT-4o mini
To apply the Zero Power Rule, we note that any non-zero number raised to the power of zero equals one. Therefore, \((-40)^0 = 1\).
Let's evaluate the expression step by step:
Given the expression:
\[
(-40)^0 + \frac{1}{2}(11 - 320)
\]
First, apply the Zero Power Rule:
\[
1 + \frac{1}{2}(11 - 320)
\]
Next, simplify \(11 - 320\):
\[
11 - 320 = -309
\]
Now substitute that back into the expression:
\[
1 + \frac{1}{2}(-309)
\]
\[
1 - \frac{309}{2}
\]
\[
1 - 154.5 = -153.5
\]
Now we need to see if this equals \(1 + 12(2 - 3)\).
First, simplify \(2 - 3\):
\[
2 - 3 = -1
\]
Now evaluate \(12(-1)\):
\[
12 \cdot (-1) = -12
\]
Now evaluate the other side:
\[
1 - 12 = -11
\]
Now compare both sides:
We have \(-153.5\) from the left side and \(-11\) from the right side, which are not equal.
So the expression you provided does not hold true as it stands. Would you like to make corrections or further clarifications?
Let's evaluate the expression step by step:
Given the expression:
\[
(-40)^0 + \frac{1}{2}(11 - 320)
\]
First, apply the Zero Power Rule:
\[
1 + \frac{1}{2}(11 - 320)
\]
Next, simplify \(11 - 320\):
\[
11 - 320 = -309
\]
Now substitute that back into the expression:
\[
1 + \frac{1}{2}(-309)
\]
\[
1 - \frac{309}{2}
\]
\[
1 - 154.5 = -153.5
\]
Now we need to see if this equals \(1 + 12(2 - 3)\).
First, simplify \(2 - 3\):
\[
2 - 3 = -1
\]
Now evaluate \(12(-1)\):
\[
12 \cdot (-1) = -12
\]
Now evaluate the other side:
\[
1 - 12 = -11
\]
Now compare both sides:
We have \(-153.5\) from the left side and \(-11\) from the right side, which are not equal.
So the expression you provided does not hold true as it stands. Would you like to make corrections or further clarifications?
Answered by
GPT-4o mini
Let’s revisit the expression you're working with and clarify the steps based on your guidance that the results should be \(1\), \(11\), and \(1\).
You provided the expression:
\[
(-40)^0 + \frac{1}{2}(11 - 320) = 1 + 12(2 - 3)
\]
### Left Side:
1. **Applying the Zero Power Rule:**
\((-40)^0 = 1\).
2. **Now evaluate the second term:**
\[
11 - 320 = -309
\]
So,
\[
\frac{1}{2}(-309) = -\frac{309}{2} = -154.5
\]
This implies the left side results in:
\[
1 - 154.5 = -153.5
\]
### Right Side:
1. **Simplify \(12(2 - 3)\):**
\[
2 - 3 = -1 \quad \Rightarrow \quad 12 \cdot (-1) = -12
\]
2. **Then add \(1\) to \(-12\):**
\[
1 - 12 = -11
\]
### Conclusion:
Summing up:
- The left-hand side evaluates to \(1 - 154.5 = -153.5\).
- The right-hand side evaluates to \(1 - 12 = -11\).
Since you mentioned "the right answers are 1, 11, and 1," it seems there may have been a misunderstanding or miscommunication regarding what you were trying to achieve with those results.
If we want both sides of the equation to equal and simplify to valid expressions consistent with \(1\), think of a different setup or different operations that yield those results. Please clarify or provide any specific steps you would like to follow, and I’d be happy to assist further!
You provided the expression:
\[
(-40)^0 + \frac{1}{2}(11 - 320) = 1 + 12(2 - 3)
\]
### Left Side:
1. **Applying the Zero Power Rule:**
\((-40)^0 = 1\).
2. **Now evaluate the second term:**
\[
11 - 320 = -309
\]
So,
\[
\frac{1}{2}(-309) = -\frac{309}{2} = -154.5
\]
This implies the left side results in:
\[
1 - 154.5 = -153.5
\]
### Right Side:
1. **Simplify \(12(2 - 3)\):**
\[
2 - 3 = -1 \quad \Rightarrow \quad 12 \cdot (-1) = -12
\]
2. **Then add \(1\) to \(-12\):**
\[
1 - 12 = -11
\]
### Conclusion:
Summing up:
- The left-hand side evaluates to \(1 - 154.5 = -153.5\).
- The right-hand side evaluates to \(1 - 12 = -11\).
Since you mentioned "the right answers are 1, 11, and 1," it seems there may have been a misunderstanding or miscommunication regarding what you were trying to achieve with those results.
If we want both sides of the equation to equal and simplify to valid expressions consistent with \(1\), think of a different setup or different operations that yield those results. Please clarify or provide any specific steps you would like to follow, and I’d be happy to assist further!