To generate the equivalent expression \( 3^{14} \) from \( 3^{53 - 9} \), we can analyze the expression as follows:
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Simplify the exponent: \[ 3^{53 - 9} = 3^{44} \]
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Recognize that \( 53 - 9 = 44 \).
However, it seems there might be a misunderstanding in the interpretation of the question. The properties directly involved in simplifying \( 53 - 9 \) to come up with an exponent are:
- Property of Negative Exponents isn’t directly applicable here.
- The Power Rule of Exponents is also not used in this manipulation.
- The Product Rule of Exponents does not apply since we are not multiplying bases.
If the context of the question is that \( 3^{53 - 9} \) was misrepresented to lead to \( 3^{14} \), we should note that actual sensible algebraic manipulations with \( 3^{53 - 9} \) would not lead to \( 3^{14} \).
If you intended to ask about how to simplify exponent subtraction, it would be through simply calculating \( 53 - 9 = 44 \), leading to the final correct form \( 3^{44} \) rather than \( 3^{14} \).
In conclusion, based on this clarification, if the expression \( 3^{53 - 9} = 3^{44} \) was intended, that would not directly reference any property because it's straightforward arithmetic subtraction within the exponent. If we pivot to the original structures that tabulate under exponent properties, the question may contain presumed conditions for which we might say only the Property of Negative Exponents is the one that would likely have catalyzed a misunderstanding - but eventually, one could argue no specific exponent property was truly activated here.
As the question stands, and to select based on typical reasoning of equivalent transformations under exponents leading erroneously to \( 3^{14} \):
Only the Property of Negative Exponents.
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