Question
How can you rewrite 21−−√3
using a rational exponent?(1 point)
Responses
2113
21 superscript Start Fraction 1 over 3 End Fraction baseline
211
21 superscript 1 baseline
321
3 superscript 21 baseline
213
using a rational exponent?(1 point)
Responses
2113
21 superscript Start Fraction 1 over 3 End Fraction baseline
211
21 superscript 1 baseline
321
3 superscript 21 baseline
213
Answers
GPT-4o mini
To rewrite \( 21 \sqrt[3]{3} \) using a rational exponent, we start by recognizing that the radical can be expressed as an exponent. The cube root of \( 3 \) can be written as \( 3^{1/3} \).
Thus, \( 21 \sqrt[3]{3} \) can be rewritten as:
\[
21 \cdot 3^{1/3}
\]
However, the original expression \( 21 \sqrt[3]{3} \) does not equate to any of the provided responses directly unless we restate it.
Assuming you meant \( 21 \cdot 3^{1/3} \) with an implication regarding the exponents:
The term \( 21 \) can also be expressed as \( 21^{1} \).
So the correct expression can combine these two things:
The closest match for \( 21 \sqrt[3]{3} \) in a form that uses rational exponents is:
- **\( 21^{1} \cdot 3^{1/3} \)**, but that was not among the answer choices given.
Looking at the choices:
1. \( 21^{1/3} \) (this isn't correct)
2. \( 21 \) (this is not an exponent form)
3. \( 3^{21} \) (this is not correct)
4. \( 21^{1} \) (just the number, but with an exponent)
The best conclusion, given the responses you provided, seems that there might be a misunderstanding with the options.
However, considering the desire for a direct match, among the possible interpretations, the new expression for \( \sqrt[3]{3} \) becomes clearer, but none of the options might fit your earlier intentions directly. The closest correct expression to provide would be something like \( 21 \cdot 3^{1/3} \).
If the options are meant to reformulate in a rational exponent format, you might want to double-check them to ensure everything is aligned properly.
Thus, \( 21 \sqrt[3]{3} \) can be rewritten as:
\[
21 \cdot 3^{1/3}
\]
However, the original expression \( 21 \sqrt[3]{3} \) does not equate to any of the provided responses directly unless we restate it.
Assuming you meant \( 21 \cdot 3^{1/3} \) with an implication regarding the exponents:
The term \( 21 \) can also be expressed as \( 21^{1} \).
So the correct expression can combine these two things:
The closest match for \( 21 \sqrt[3]{3} \) in a form that uses rational exponents is:
- **\( 21^{1} \cdot 3^{1/3} \)**, but that was not among the answer choices given.
Looking at the choices:
1. \( 21^{1/3} \) (this isn't correct)
2. \( 21 \) (this is not an exponent form)
3. \( 3^{21} \) (this is not correct)
4. \( 21^{1} \) (just the number, but with an exponent)
The best conclusion, given the responses you provided, seems that there might be a misunderstanding with the options.
However, considering the desire for a direct match, among the possible interpretations, the new expression for \( \sqrt[3]{3} \) becomes clearer, but none of the options might fit your earlier intentions directly. The closest correct expression to provide would be something like \( 21 \cdot 3^{1/3} \).
If the options are meant to reformulate in a rational exponent format, you might want to double-check them to ensure everything is aligned properly.