To rewrite \( 21 - \sqrt{3} \) using a rational exponent, we need to express the square root in terms of an exponent.
The square root can be expressed as a rational exponent:
\[ \sqrt{3} = 3^{1/2} \]
Thus, \( 21 - \sqrt{3} \) can be written as:
\[ 21 - 3^{1/2} \]
However, from the options provided, it seems we are looking for a way to express \( 21 - \sqrt{3} \) in terms of a rational exponent without losing its form. None of the responses directly express \( 21 - \sqrt{3} \), but we can simplify and identify the options based on rational exponents.
Since there are no direct equivalent forms for \( 21 - \sqrt{3} \) using the provided exponents, it appears that the options given do not represent the expression directly.
If the question is instead asking about how to represent \( \sqrt{3} \) as a rational exponent in relation to \( 21 \), the simplified expression we can pull from here for clarity within the limits of this choice framework would be:
The best choice in alignment, as per responses listed, might be referencing how square roots correlate back to rational exponent notation. However, none would correspond correctly to the full expression \( 21 - \sqrt{3} \).
If you want an interpretation focusing solely on action from presented answers focused on the direct rational exponent form without ensuring it is purely equivalent to initial \( 21 - \sqrt{3} \):
- \( 3^{21} \) or \( 3^{21/2} \) aren’t directly corresponding.
- Correspondent explanations would differ, hence the answers may be misaligned with the actual aim of simplifying given expression correctly.
Kindly clarify if the expression alteration or rational exponent focus aligns distinctly with provided options \( ( 21 + \sqrt{3} \)` within addressed terms of rational exponent needs hence.
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