Question
Apply the Zero Power Rule to create an equivalent expression to (−40)^0 + 1/2(11−32^0) (−40)^0 + 1/2(11−32^0) = 1 +12 (2 − 3 )
Answers
Answer
NO THE RIGHT ANSERS ARE 1,11,1
Answer
(−40)^0 + 1/2(11−32^0) = blank +1/2 (blank− blank)
Answer
can put on how to do it where I can copy and paste it
Answered by
GPT-4o mini
To apply the Zero Power Rule, we note that any non-zero number raised to the power of 0 equals 1. Specifically:
\[
(-40)^0 = 1 \quad \text{and} \quad 32^0 = 1
\]
Now we can rewrite the expression \( (-40)^0 + \frac{1}{2}(11 - 32^0) \):
1. Replace \((-40)^0\) with \(1\):
\[
1 + \frac{1}{2}(11 - 1)
\]
2. Simplify inside the parentheses:
\[
11 - 1 = 10
\]
So the expression becomes:
\[
1 + \frac{1}{2}(10)
\]
3. Calculate \(\frac{1}{2}(10)\):
\[
\frac{1}{2}(10) = 5
\]
Now putting it all together:
\[
1 + 5 = 6
\]
Thus, the equivalent expression to \((-40)^0 + \frac{1}{2}(11 - 32^0)\) is:
\[
6
\]
Next, we look at the right side of the equation you provided, which is \(1 + 12(2 - 3)\):
1. Calculate \(2 - 3\):
\[
2 - 3 = -1
\]
2. Now multiply:
\[
12(-1) = -12
\]
3. Finally, add \(1\):
\[
1 - 12 = -11
\]
So, the expression \(1 + 12(2 - 3)\) evaluates to:
\[
-11
\]
In conclusion, we have:
\[
(-40)^0 + \frac{1}{2}(11 - 32^0) = 6
\]
\[
1 + 12(2 - 3) = -11
\]
These two sides are not equal, which means the original statement that they are equivalent does not hold true. The correct answers are:
\[
(-40)^0 + \frac{1}{2}(11 - 32^0) = 6
\]
\[
1 + 12(2 - 3) = -11
\]
\[
(-40)^0 = 1 \quad \text{and} \quad 32^0 = 1
\]
Now we can rewrite the expression \( (-40)^0 + \frac{1}{2}(11 - 32^0) \):
1. Replace \((-40)^0\) with \(1\):
\[
1 + \frac{1}{2}(11 - 1)
\]
2. Simplify inside the parentheses:
\[
11 - 1 = 10
\]
So the expression becomes:
\[
1 + \frac{1}{2}(10)
\]
3. Calculate \(\frac{1}{2}(10)\):
\[
\frac{1}{2}(10) = 5
\]
Now putting it all together:
\[
1 + 5 = 6
\]
Thus, the equivalent expression to \((-40)^0 + \frac{1}{2}(11 - 32^0)\) is:
\[
6
\]
Next, we look at the right side of the equation you provided, which is \(1 + 12(2 - 3)\):
1. Calculate \(2 - 3\):
\[
2 - 3 = -1
\]
2. Now multiply:
\[
12(-1) = -12
\]
3. Finally, add \(1\):
\[
1 - 12 = -11
\]
So, the expression \(1 + 12(2 - 3)\) evaluates to:
\[
-11
\]
In conclusion, we have:
\[
(-40)^0 + \frac{1}{2}(11 - 32^0) = 6
\]
\[
1 + 12(2 - 3) = -11
\]
These two sides are not equal, which means the original statement that they are equivalent does not hold true. The correct answers are:
\[
(-40)^0 + \frac{1}{2}(11 - 32^0) = 6
\]
\[
1 + 12(2 - 3) = -11
\]
Answered by
GPT-4o mini
Let's reevaluate the expression step by step with the intention of clarifying the results.
1. We start with the left side expression:
\[
(-40)^0 + \frac{1}{2}(11 - 32^0)
\]
Here, we can apply the Zero Power Rule:
- \((-40)^0 = 1\)
- \(32^0 = 1\)
So, we can rewrite the expression:
\[
1 + \frac{1}{2}(11 - 1)
\]
2. Simplify the expression inside the parentheses:
\[
11 - 1 = 10
\]
Now our expression looks like this:
\[
1 + \frac{1}{2}(10)
\]
3. Calculate \(\frac{1}{2}(10)\):
\[
\frac{1}{2} \times 10 = 5
\]
4. Combine the terms:
\[
1 + 5 = 6
\]
So, the left side evaluates to:
\[
(-40)^0 + \frac{1}{2}(11 - 32^0) = 6
\]
---
Now, let's check the right side:
\[
1 + 12(2 - 3)
\]
1. Calculate \(2 - 3\):
\[
2 - 3 = -1
\]
2. Now multiply by 12:
\[
12 \times (-1) = -12
\]
3. Finally, add 1:
\[
1 - 12 = -11
\]
So, the right side evaluates to:
\[
1 + 12(2 - 3) = -11
\]
To summarize:
- Left side: \(6\)
- Right side: \(-11\)
Based on the calculations above, the two sides are not equal, so it's unclear where the values \(1\), \(11\), and \(1\) are coming from.
If you could clarify your context or what specific parts you want to remain equivalent, I would be glad to assist you further!
1. We start with the left side expression:
\[
(-40)^0 + \frac{1}{2}(11 - 32^0)
\]
Here, we can apply the Zero Power Rule:
- \((-40)^0 = 1\)
- \(32^0 = 1\)
So, we can rewrite the expression:
\[
1 + \frac{1}{2}(11 - 1)
\]
2. Simplify the expression inside the parentheses:
\[
11 - 1 = 10
\]
Now our expression looks like this:
\[
1 + \frac{1}{2}(10)
\]
3. Calculate \(\frac{1}{2}(10)\):
\[
\frac{1}{2} \times 10 = 5
\]
4. Combine the terms:
\[
1 + 5 = 6
\]
So, the left side evaluates to:
\[
(-40)^0 + \frac{1}{2}(11 - 32^0) = 6
\]
---
Now, let's check the right side:
\[
1 + 12(2 - 3)
\]
1. Calculate \(2 - 3\):
\[
2 - 3 = -1
\]
2. Now multiply by 12:
\[
12 \times (-1) = -12
\]
3. Finally, add 1:
\[
1 - 12 = -11
\]
So, the right side evaluates to:
\[
1 + 12(2 - 3) = -11
\]
To summarize:
- Left side: \(6\)
- Right side: \(-11\)
Based on the calculations above, the two sides are not equal, so it's unclear where the values \(1\), \(11\), and \(1\) are coming from.
If you could clarify your context or what specific parts you want to remain equivalent, I would be glad to assist you further!
Answered by
GPT-4o mini
Let's simplify the expression step-by-step while breaking it down into the format you have provided:
**The original expression is:**
\[
(-40)^0 + \frac{1}{2}(11 - 32^0)
\]
### Step 1: Apply the Zero Power Rule
Using the Zero Power Rule:
- \((-40)^0 = 1\)
- \(32^0 = 1\)
### Step 2: Substitute These Values Back into the Expression
This transforms the expression to:
\[
1 + \frac{1}{2}(11 - 1)
\]
### Step 3: Simplify Inside the Parentheses
Now, calculate \(11 - 1\):
\[
11 - 1 = 10
\]
### Step 4: Substitute Back Into the Expression
Now substituting back, we have:
\[
1 + \frac{1}{2}(10)
\]
### Step 5: Calculate \(\frac{1}{2}(10)\)
Calculating \(\frac{1}{2}(10)\):
\[
\frac{1}{2}(10) = 5
\]
### Step 6: Complete the Original Expression
Now we can finish the original expression:
\[
1 + 5 = 6
\]
---
Now, you wanted to express this in the format of:
\[
\text{blank} + \frac{1}{2}(\text{blank} - \text{blank})
\]
### Filling the Blanks
Looking at the original form you wanted:
1. The first blank corresponds to \((-40)^0\), which is \(1\).
2. The second blank corresponds to \(11\).
3. The third blank corresponds to \(32^0\), which is \(1\).
Thus, we fill in the blanks as follows:
### Final Result
The expression can be rewritten as:
\[
1 + \frac{1}{2}(11 - 1)
\]
So, filled in, it looks like this:
\[
1 + \frac{1}{2}(11 - 1)
\]
This maintains the equivalence and matches the format you requested. The final answer is:
\[
1 + \frac{1}{2}(11 - 1)
\]
Please let me know if you need further assistance!
**The original expression is:**
\[
(-40)^0 + \frac{1}{2}(11 - 32^0)
\]
### Step 1: Apply the Zero Power Rule
Using the Zero Power Rule:
- \((-40)^0 = 1\)
- \(32^0 = 1\)
### Step 2: Substitute These Values Back into the Expression
This transforms the expression to:
\[
1 + \frac{1}{2}(11 - 1)
\]
### Step 3: Simplify Inside the Parentheses
Now, calculate \(11 - 1\):
\[
11 - 1 = 10
\]
### Step 4: Substitute Back Into the Expression
Now substituting back, we have:
\[
1 + \frac{1}{2}(10)
\]
### Step 5: Calculate \(\frac{1}{2}(10)\)
Calculating \(\frac{1}{2}(10)\):
\[
\frac{1}{2}(10) = 5
\]
### Step 6: Complete the Original Expression
Now we can finish the original expression:
\[
1 + 5 = 6
\]
---
Now, you wanted to express this in the format of:
\[
\text{blank} + \frac{1}{2}(\text{blank} - \text{blank})
\]
### Filling the Blanks
Looking at the original form you wanted:
1. The first blank corresponds to \((-40)^0\), which is \(1\).
2. The second blank corresponds to \(11\).
3. The third blank corresponds to \(32^0\), which is \(1\).
Thus, we fill in the blanks as follows:
### Final Result
The expression can be rewritten as:
\[
1 + \frac{1}{2}(11 - 1)
\]
So, filled in, it looks like this:
\[
1 + \frac{1}{2}(11 - 1)
\]
This maintains the equivalence and matches the format you requested. The final answer is:
\[
1 + \frac{1}{2}(11 - 1)
\]
Please let me know if you need further assistance!
Answered by
GPT-4o mini
Sure! Below is a clear and formatted step-by-step breakdown that you can easily copy and paste:
---
### Given Expression
\[
(-40)^0 + \frac{1}{2}(11 - 32^0)
\]
### Step 1: Apply the Zero Power Rule
Using the Zero Power Rule:
- \((-40)^0 = 1\)
- \(32^0 = 1\)
### New Expression
Substituting these values gives:
\[
1 + \frac{1}{2}(11 - 1)
\]
### Step 2: Simplify Inside the Parentheses
Calculate \(11 - 1\):
\[
11 - 1 = 10
\]
### New Expression
Now we substitute back:
\[
1 + \frac{1}{2}(10)
\]
### Step 3: Calculate \(\frac{1}{2}(10)\)
This equals:
\[
\frac{1}{2}(10) = 5
\]
### Final Expression
Combine the terms:
\[
1 + 5 = 6
\]
---
### Filling the Blanks
To represent it in the requested format:
\[
\text{blank} + \frac{1}{2}(\text{blank} - \text{blank})
\]
### Filling in the Blanks:
1. **First blank:** \(1\) (which is \((-40)^0\))
2. **Second blank:** \(11\)
3. **Third blank:** \(1\) (which is \(32^0\))
### Final Form
So your expression can be written as:
\[
1 + \frac{1}{2}(11 - 1)
\]
You can simply copy and paste the formatted version above. If more details are needed, feel free to ask!
---
### Given Expression
\[
(-40)^0 + \frac{1}{2}(11 - 32^0)
\]
### Step 1: Apply the Zero Power Rule
Using the Zero Power Rule:
- \((-40)^0 = 1\)
- \(32^0 = 1\)
### New Expression
Substituting these values gives:
\[
1 + \frac{1}{2}(11 - 1)
\]
### Step 2: Simplify Inside the Parentheses
Calculate \(11 - 1\):
\[
11 - 1 = 10
\]
### New Expression
Now we substitute back:
\[
1 + \frac{1}{2}(10)
\]
### Step 3: Calculate \(\frac{1}{2}(10)\)
This equals:
\[
\frac{1}{2}(10) = 5
\]
### Final Expression
Combine the terms:
\[
1 + 5 = 6
\]
---
### Filling the Blanks
To represent it in the requested format:
\[
\text{blank} + \frac{1}{2}(\text{blank} - \text{blank})
\]
### Filling in the Blanks:
1. **First blank:** \(1\) (which is \((-40)^0\))
2. **Second blank:** \(11\)
3. **Third blank:** \(1\) (which is \(32^0\))
### Final Form
So your expression can be written as:
\[
1 + \frac{1}{2}(11 - 1)
\]
You can simply copy and paste the formatted version above. If more details are needed, feel free to ask!