To generate the expression \( 3^{14} \) from \( 3^{53 - 9} \), we can simplify \( 53 - 9 \) as follows:
\[ 53 - 9 = 44 \]
Thus,
\[ 3^{53 - 9} = 3^{44} \]
However, it seems that there's confusion here. If you meant \( 3^{53} \cdot 3^{-9} \) to reach \( 3^{14} \), then we would use:
- The Product Rule of Exponents, which states that \( a^m \cdot a^n = a^{m+n} \).
- The Property of Negative Exponents, which states that \( a^{-n} = \frac{1}{a^n} \).
Using these rules, we would have:
\[ 3^{53} \cdot 3^{-9} = 3^{53 + (-9)} = 3^{53 - 9} = 3^{44} \]
So, if our goal was to reach \( 3^{14} \), we could think of it in the same way where \( 3^{53} \cdot 3^{-39} = 3^{53 + (-39)} = 3^{14} \).
Given the responses you provided, the best possible choice would be:
the Property of Negative Exponents and the Product Rule of Exponents.
Thus, this would be the most appropriate selection from your options!
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