Question
Which of the following is developed to be equivalent to 1/8 5
?(1 point)
Responses
815
8 Start Fraction 1 over 5 End Fraction
5−8
5 superscript negative 8 baseline
85
8 superscript 5 baseline
8−5
8 superscript negative 5 baseline
Skip to navigation
?(1 point)
Responses
815
8 Start Fraction 1 over 5 End Fraction
5−8
5 superscript negative 8 baseline
85
8 superscript 5 baseline
8−5
8 superscript negative 5 baseline
Skip to navigation
Answers
Answer
its 1/8 with 8 to the power of 5
Answer
no its 1/8 to the power of 5
Answer
1
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8 5
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8 5
Answered by
GPT-4o mini
To determine which expression is equivalent to \( \frac{1}{8} \cdot 5 \), we can rewrite it in a simpler form:
\[
\frac{1}{8} \cdot 5 = \frac{5}{8}
\]
Now let's analyze each of the given options:
1. **\( 8 \frac{1}{5} \)** is a mixed number, which is not equivalent to \( \frac{5}{8} \).
2. **\( 5^{-8} \)** is equivalent to \( \frac{1}{5^8} \), which is also not equivalent to \( \frac{5}{8} \).
3. **\( 8^5 \)** is simply \( 8 \) raised to the power of \( 5 \), which is not equivalent to \( \frac{5}{8} \).
4. **\( 8^{-5} \)** is equivalent to \( \frac{1}{8^5} \), which again is not equivalent to \( \frac{5}{8} \).
None of the provided options are equivalent to \( \frac{5}{8} \) or \( \frac{1}{8} \cdot 5 \). Therefore, the correct answer from the options you provided is:
- None of these are equivalent to \( \frac{1}{8} \cdot 5 \).
\[
\frac{1}{8} \cdot 5 = \frac{5}{8}
\]
Now let's analyze each of the given options:
1. **\( 8 \frac{1}{5} \)** is a mixed number, which is not equivalent to \( \frac{5}{8} \).
2. **\( 5^{-8} \)** is equivalent to \( \frac{1}{5^8} \), which is also not equivalent to \( \frac{5}{8} \).
3. **\( 8^5 \)** is simply \( 8 \) raised to the power of \( 5 \), which is not equivalent to \( \frac{5}{8} \).
4. **\( 8^{-5} \)** is equivalent to \( \frac{1}{8^5} \), which again is not equivalent to \( \frac{5}{8} \).
None of the provided options are equivalent to \( \frac{5}{8} \) or \( \frac{1}{8} \cdot 5 \). Therefore, the correct answer from the options you provided is:
- None of these are equivalent to \( \frac{1}{8} \cdot 5 \).
Answered by
GPT-4o mini
Thank you for the clarification! It appears you meant **\( \frac{1}{8} \cdot 8^5 \)**. Let's evaluate that expression:
1. First, note that \( 8 \) can be expressed as \( 8^1 \).
2. So, \( \frac{1}{8} \cdot 8^5 = \frac{8^5}{8^1} \).
3. Using the property of exponents, \( \frac{8^5}{8^1} = 8^{5-1} = 8^4 \).
However, since you said \( \frac{1}{8} \) with \( 8^5 \), let's rewrite and analyze the response you are considering:
- The expression \( \frac{1}{8} \cdot 8^5\) indeed simplifies to \( 8^4\), which can further be analyzed if you consider what \( \frac{1}{8} \) means in another context.
If there’s a specific response or format you are referencing that matches that \( \frac{1}{8} \cdot 8^5 \), please let me know! Otherwise, based on the options provided in your previous message, the only relevant representation of this alongside exponential understanding would still align with basic simplification.
If you want to ask further about the comparisons or clarity on any other expressions in your exam, please let me know!
1. First, note that \( 8 \) can be expressed as \( 8^1 \).
2. So, \( \frac{1}{8} \cdot 8^5 = \frac{8^5}{8^1} \).
3. Using the property of exponents, \( \frac{8^5}{8^1} = 8^{5-1} = 8^4 \).
However, since you said \( \frac{1}{8} \) with \( 8^5 \), let's rewrite and analyze the response you are considering:
- The expression \( \frac{1}{8} \cdot 8^5\) indeed simplifies to \( 8^4\), which can further be analyzed if you consider what \( \frac{1}{8} \) means in another context.
If there’s a specific response or format you are referencing that matches that \( \frac{1}{8} \cdot 8^5 \), please let me know! Otherwise, based on the options provided in your previous message, the only relevant representation of this alongside exponential understanding would still align with basic simplification.
If you want to ask further about the comparisons or clarity on any other expressions in your exam, please let me know!
Answered by
GPT-4o mini
Thank you for your patience! If you're referring to \( \left(\frac{1}{8}\right)^5 \) or \( \frac{1}{8^5} \), let's clarify that:
\[
\left(\frac{1}{8}\right)^5 = \frac{1^5}{8^5} = \frac{1}{8^5}
\]
This effectively indicates raising \( \frac{1}{8} \) to the power of \( 5\).
Now let’s analyze which of the responses provided matches this:
1. **\( 8 \frac{1}{5} \)** (This is a mixed number and not equivalent)
2. **\( 5^{-8} \)** (This is equivalent to \( \frac{1}{5^8} \), not equivalent)
3. **\( 8^5 \)** (This is just \( 8 \) raised to the power of \( 5\), not equivalent)
4. **\( 8^{-5} \)** (This is equivalent to \( \frac{1}{8^5} \), which is indeed equivalent to \( \left(\frac{1}{8}\right)^5\))
So the correct response from your original question that matches \( \left(\frac{1}{8}\right)^5 \) would be:
**\( 8^{-5} \)**
Thank you for your corrections, and I hope this clarification helps! If you have further questions, feel free to ask.
\[
\left(\frac{1}{8}\right)^5 = \frac{1^5}{8^5} = \frac{1}{8^5}
\]
This effectively indicates raising \( \frac{1}{8} \) to the power of \( 5\).
Now let’s analyze which of the responses provided matches this:
1. **\( 8 \frac{1}{5} \)** (This is a mixed number and not equivalent)
2. **\( 5^{-8} \)** (This is equivalent to \( \frac{1}{5^8} \), not equivalent)
3. **\( 8^5 \)** (This is just \( 8 \) raised to the power of \( 5\), not equivalent)
4. **\( 8^{-5} \)** (This is equivalent to \( \frac{1}{8^5} \), which is indeed equivalent to \( \left(\frac{1}{8}\right)^5\))
So the correct response from your original question that matches \( \left(\frac{1}{8}\right)^5 \) would be:
**\( 8^{-5} \)**
Thank you for your corrections, and I hope this clarification helps! If you have further questions, feel free to ask.
Answered by
GPT-4o mini
Thank you for your clarification. It seems you are referring to the notation **\( \frac{1}{8^5} \)**, which can also be expressed as \( 1 / (8^5) \).
To summarize:
- **\( \frac{1}{8^5} \)** or **\( 8^{-5} \)** both represent the same mathematical value, as \( 8^{-5} = \frac{1}{8^5} \).
So, in the context of your provided responses, the option that corresponds to **\( \frac{1}{8^5} \)** would indeed be:
- **\( 8^{-5} \)**.
If you have any more questions or need further assistance, feel free to ask!
To summarize:
- **\( \frac{1}{8^5} \)** or **\( 8^{-5} \)** both represent the same mathematical value, as \( 8^{-5} = \frac{1}{8^5} \).
So, in the context of your provided responses, the option that corresponds to **\( \frac{1}{8^5} \)** would indeed be:
- **\( 8^{-5} \)**.
If you have any more questions or need further assistance, feel free to ask!