Question
The equivalent expression to \((15-3\ 4^{7})^{0}\ 4^{-3}\).
Answers
Answer
Nope
Answer
its 60
Answered by
GPT-4o mini
To simplify the expression \((15 - 3 \cdot 4^{7})^{0} \cdot 4^{-3}\), we start by simplifying each part.
1. **Simplifying \((15 - 3 \cdot 4^{7})^{0}\):**
Any expression raised to the power of \(0\) is equal to \(1\) (as long as the base is not zero). Therefore,
\[
(15 - 3 \cdot 4^{7})^{0} = 1.
\]
2. **Simplifying \(4^{-3}\):**
The expression \(4^{-3}\) can be converted to its positive exponent form:
\[
4^{-3} = \frac{1}{4^{3}}.
\]
Now, calculate \(4^{3}\):
\[
4^{3} = 64.
\]
Therefore,
\[
4^{-3} = \frac{1}{64}.
\]
3. **Combining the results:**
Now we can substitute back into the overall expression:
\[
(15 - 3 \cdot 4^{7})^{0} \cdot 4^{-3} = 1 \cdot \frac{1}{64} = \frac{1}{64}.
\]
Thus, the equivalent expression to \((15 - 3 \cdot 4^{7})^{0} \cdot 4^{-3}\) is:
\[
\boxed{\frac{1}{64}}.
\]
1. **Simplifying \((15 - 3 \cdot 4^{7})^{0}\):**
Any expression raised to the power of \(0\) is equal to \(1\) (as long as the base is not zero). Therefore,
\[
(15 - 3 \cdot 4^{7})^{0} = 1.
\]
2. **Simplifying \(4^{-3}\):**
The expression \(4^{-3}\) can be converted to its positive exponent form:
\[
4^{-3} = \frac{1}{4^{3}}.
\]
Now, calculate \(4^{3}\):
\[
4^{3} = 64.
\]
Therefore,
\[
4^{-3} = \frac{1}{64}.
\]
3. **Combining the results:**
Now we can substitute back into the overall expression:
\[
(15 - 3 \cdot 4^{7})^{0} \cdot 4^{-3} = 1 \cdot \frac{1}{64} = \frac{1}{64}.
\]
Thus, the equivalent expression to \((15 - 3 \cdot 4^{7})^{0} \cdot 4^{-3}\) is:
\[
\boxed{\frac{1}{64}}.
\]
Answered by
GPT-4o mini
Let's carefully re-evaluate the expression \((15 - 3\cdot 4^{7})^{0} \cdot 4^{-3}\).
1. **Evaluate \((15 - 3\cdot 4^{7})^{0}\)**:
Any non-zero expression raised to the power of \(0\) equals \(1\). However, we need to check if \(15 - 3\cdot 4^{7}\) is zero:
\[
4^{7} = 16384 \quad \text{(since } 4^{3} = 64 \text{ and } 4^{6} = 4096 \text{, yielding } 4^{7} = 4 \cdot 4096\text{)}
\]
Therefore,
\[
3 \cdot 4^{7} = 3 \cdot 16384 = 49152.
\]
So,
\[
15 - 49152 = -49137.
\]
Since \(-49137 \neq 0\), we have:
\[
(15 - 3 \cdot 4^{7})^{0} = 1.
\]
2. **Evaluate \(4^{-3}\)**:
This can be simplified as:
\[
4^{-3} = \frac{1}{4^{3}} = \frac{1}{64}.
\]
3. **Combine the Results**:
Now combining the results from steps 1 and 2:
\[
(15 - 3\cdot 4^{7})^{0} \cdot 4^{-3} = 1 \cdot \frac{1}{64} = \frac{1}{64}.
\]
Thus, the final result is indeed:
\[
\boxed{\frac{1}{64}}.
\]
If this result is still not what you were looking for, please let me know how you would like to approach it or clarify any additional context!
1. **Evaluate \((15 - 3\cdot 4^{7})^{0}\)**:
Any non-zero expression raised to the power of \(0\) equals \(1\). However, we need to check if \(15 - 3\cdot 4^{7}\) is zero:
\[
4^{7} = 16384 \quad \text{(since } 4^{3} = 64 \text{ and } 4^{6} = 4096 \text{, yielding } 4^{7} = 4 \cdot 4096\text{)}
\]
Therefore,
\[
3 \cdot 4^{7} = 3 \cdot 16384 = 49152.
\]
So,
\[
15 - 49152 = -49137.
\]
Since \(-49137 \neq 0\), we have:
\[
(15 - 3 \cdot 4^{7})^{0} = 1.
\]
2. **Evaluate \(4^{-3}\)**:
This can be simplified as:
\[
4^{-3} = \frac{1}{4^{3}} = \frac{1}{64}.
\]
3. **Combine the Results**:
Now combining the results from steps 1 and 2:
\[
(15 - 3\cdot 4^{7})^{0} \cdot 4^{-3} = 1 \cdot \frac{1}{64} = \frac{1}{64}.
\]
Thus, the final result is indeed:
\[
\boxed{\frac{1}{64}}.
\]
If this result is still not what you were looking for, please let me know how you would like to approach it or clarify any additional context!
Answered by
GPT-4o mini
I apologize for the confusion. Let's break down the expression \( (15 - 3 \cdot 4^{7})^{0} \cdot 4^{-3} \) step-by-step more clearly to verify the calculations.
1. **Evaluate the expression inside the parentheses**:
\[
4^7 = 16384 \quad \text{(since \(4^7 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4\))}
\]
2. **Calculate \(3 \cdot 4^7\)**:
\[
3 \cdot 16384 = 49152.
\]
3. **Now, compute \(15 - 3 \cdot 4^7\)**:
\[
15 - 49152 = 15 - 49152 = -49137.
\]
4. **Evaluate \((15 - 3 \cdot 4^7)^0\)**:
Since \(-49137\) is not zero, we have:
\[
(15 - 3 \cdot 4^7)^0 = 1.
\]
5. **Next, calculate \(4^{-3}\)**:
\[
4^{-3} = \frac{1}{4^3} = \frac{1}{64}.
\]
6. **Combine the results**:
\[
(15 - 3 \cdot 4^{7})^{0} \cdot 4^{-3} = 1 \cdot \frac{1}{64} = \frac{1}{64}.
\]
The calculations confirm that the final result is \(\frac{1}{64}\).
However, if you mentioned "60," let's check if a different interpretation of the expression was intended or if there's any additional operation or modification to the expression.
If there’s a specific correction you want me to address or a different expression to evaluate that results in 60, please let me know!
1. **Evaluate the expression inside the parentheses**:
\[
4^7 = 16384 \quad \text{(since \(4^7 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4\))}
\]
2. **Calculate \(3 \cdot 4^7\)**:
\[
3 \cdot 16384 = 49152.
\]
3. **Now, compute \(15 - 3 \cdot 4^7\)**:
\[
15 - 49152 = 15 - 49152 = -49137.
\]
4. **Evaluate \((15 - 3 \cdot 4^7)^0\)**:
Since \(-49137\) is not zero, we have:
\[
(15 - 3 \cdot 4^7)^0 = 1.
\]
5. **Next, calculate \(4^{-3}\)**:
\[
4^{-3} = \frac{1}{4^3} = \frac{1}{64}.
\]
6. **Combine the results**:
\[
(15 - 3 \cdot 4^{7})^{0} \cdot 4^{-3} = 1 \cdot \frac{1}{64} = \frac{1}{64}.
\]
The calculations confirm that the final result is \(\frac{1}{64}\).
However, if you mentioned "60," let's check if a different interpretation of the expression was intended or if there's any additional operation or modification to the expression.
If there’s a specific correction you want me to address or a different expression to evaluate that results in 60, please let me know!
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