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Original Question
Simplify 13 with an exponent of 12 divided by 13 with an exponent of -10.Question
simplify 4 with an exponent of 13 divided by 3 with an exponent of -5
Answers
Answered by
GPT-4o mini
To simplify the expression \( \frac{4^{13}}{3^{-5}} \), we can start by recalling that dividing by a negative exponent is equivalent to multiplying by the positive exponent:
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5}
\]
Now, we can express it as:
\[
4^{13} \cdot 3^{5}
\]
At this point, there isn't a standard way to simplify \( 4^{13} \cdot 3^{5} \) further without calculating the actual numerical values. However, if you need it in terms of powers, it can just remain as:
\[
4^{13} \cdot 3^{5}
\]
If you would like to calculate the numerical value:
1. Calculate \( 4^{13} \).
2. Calculate \( 3^{5} \).
3. Multiply the two results.
Calculating these:
- \( 4^{13} = 67,108,864 \)
- \( 3^{5} = 243 \)
So,
\[
4^{13} \cdot 3^{5} = 67,108,864 \cdot 243 = 16,349,249,152
\]
Thus, the simplified expression is either \( 4^{13} \cdot 3^{5} \) or its numerical value \( 16,349,249,152 \).
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5}
\]
Now, we can express it as:
\[
4^{13} \cdot 3^{5}
\]
At this point, there isn't a standard way to simplify \( 4^{13} \cdot 3^{5} \) further without calculating the actual numerical values. However, if you need it in terms of powers, it can just remain as:
\[
4^{13} \cdot 3^{5}
\]
If you would like to calculate the numerical value:
1. Calculate \( 4^{13} \).
2. Calculate \( 3^{5} \).
3. Multiply the two results.
Calculating these:
- \( 4^{13} = 67,108,864 \)
- \( 3^{5} = 243 \)
So,
\[
4^{13} \cdot 3^{5} = 67,108,864 \cdot 243 = 16,349,249,152
\]
Thus, the simplified expression is either \( 4^{13} \cdot 3^{5} \) or its numerical value \( 16,349,249,152 \).
Answer
what is the simplified version
Answered by
GPT-4o mini
The expression \( \frac{4^{13}}{3^{-5}} \) simplifies to:
\[
4^{13} \cdot 3^{5}
\]
This is the simplified version in terms of powers. If you're looking for a numerical representation, we can compute it as follows:
1. \( 4^{13} = 67,108,864 \)
2. \( 3^{5} = 243 \)
Now, multiplying these two results gives:
\[
4^{13} \cdot 3^{5} = 67,108,864 \cdot 243 = 16,349,249,152
\]
Thus, the expression \( \frac{4^{13}}{3^{-5}} \) can be kept in its simplified form as \( 4^{13} \cdot 3^{5} \) or, if needed, expressed numerically as \( 16,349,249,152 \).
So, the simplified form of the expression is:
\[
4^{13} \cdot 3^{5}
\]
This is the standard way to express it without further numerical calculation.
\[
4^{13} \cdot 3^{5}
\]
This is the simplified version in terms of powers. If you're looking for a numerical representation, we can compute it as follows:
1. \( 4^{13} = 67,108,864 \)
2. \( 3^{5} = 243 \)
Now, multiplying these two results gives:
\[
4^{13} \cdot 3^{5} = 67,108,864 \cdot 243 = 16,349,249,152
\]
Thus, the expression \( \frac{4^{13}}{3^{-5}} \) can be kept in its simplified form as \( 4^{13} \cdot 3^{5} \) or, if needed, expressed numerically as \( 16,349,249,152 \).
So, the simplified form of the expression is:
\[
4^{13} \cdot 3^{5}
\]
This is the standard way to express it without further numerical calculation.
Answer
thats incorrect
Answered by
GPT-4o mini
I apologize for any confusion in my response. Let's go through the simplification of the expression \( \frac{4^{13}}{3^{-5}} \) correctly step by step.
1. **Understanding the expression**: The expression \( \frac{4^{13}}{3^{-5}} \) can be rewritten using the property of negative exponents:
\[
\frac{a}{b^{-c}} = a \cdot b^{c}
\]
Therefore,
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5}
\]
2. **Final simplified form**: As mentioned earlier, this is already in a simplified form, but if you need it shown with the bases combined (if possible) or simplified further, we look at it this way:
\[
4^{13} \cdot 3^{5}
\]
- However, there is no further simplification in terms of a single expression since \( 4 \) and \( 3 \) cannot be combined due to differing bases.
So the **correct simplified version** of the expression \( \frac{4^{13}}{3^{-5}} \) is indeed:
\[
4^{13} \cdot 3^{5}
\]
If we convert this into numerical values for clarity:
- \( 4^{13} = 67,108,864 \)
- \( 3^{5} = 243 \)
The numerical value of the multiplication is:
\[
67,108,864 \cdot 243 = 16,349,249,152
\]
However, if we are strictly simplifying the expression, the answer remains:
\[
4^{13} \cdot 3^{5}
\]
Please let me know if you are looking for something different. Thank you for your understanding!
1. **Understanding the expression**: The expression \( \frac{4^{13}}{3^{-5}} \) can be rewritten using the property of negative exponents:
\[
\frac{a}{b^{-c}} = a \cdot b^{c}
\]
Therefore,
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5}
\]
2. **Final simplified form**: As mentioned earlier, this is already in a simplified form, but if you need it shown with the bases combined (if possible) or simplified further, we look at it this way:
\[
4^{13} \cdot 3^{5}
\]
- However, there is no further simplification in terms of a single expression since \( 4 \) and \( 3 \) cannot be combined due to differing bases.
So the **correct simplified version** of the expression \( \frac{4^{13}}{3^{-5}} \) is indeed:
\[
4^{13} \cdot 3^{5}
\]
If we convert this into numerical values for clarity:
- \( 4^{13} = 67,108,864 \)
- \( 3^{5} = 243 \)
The numerical value of the multiplication is:
\[
67,108,864 \cdot 243 = 16,349,249,152
\]
However, if we are strictly simplifying the expression, the answer remains:
\[
4^{13} \cdot 3^{5}
\]
Please let me know if you are looking for something different. Thank you for your understanding!
Answer
no its not its wrong bot
Answered by
GPT-4o mini
I apologize for any confusion earlier. Let's go through the simplification step by step correctly.
You started with the expression:
\[
\frac{4^{13}}{3^{-5}}
\]
Applying the property of negative exponents, we can rewrite this as:
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5}
\]
Now we can write \(4^{13}\) in terms of its prime factorization. Since \(4 = 2^2\), we have:
\[
4^{13} = (2^2)^{13} = 2^{26}
\]
So, replacing \(4^{13}\) in our expression gives us:
\[
2^{26} \cdot 3^{5}
\]
This is the simplified form of the original expression. There is no further simplification possible without evaluating the numerical values.
So the final simplified version is:
\[
2^{26} \cdot 3^{5}
\]
Thank you for your patience, and I hope this addresses your query correctly!
You started with the expression:
\[
\frac{4^{13}}{3^{-5}}
\]
Applying the property of negative exponents, we can rewrite this as:
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5}
\]
Now we can write \(4^{13}\) in terms of its prime factorization. Since \(4 = 2^2\), we have:
\[
4^{13} = (2^2)^{13} = 2^{26}
\]
So, replacing \(4^{13}\) in our expression gives us:
\[
2^{26} \cdot 3^{5}
\]
This is the simplified form of the original expression. There is no further simplification possible without evaluating the numerical values.
So the final simplified version is:
\[
2^{26} \cdot 3^{5}
\]
Thank you for your patience, and I hope this addresses your query correctly!