To determine how the expression \( 353 - 9 \) simplifies to \( 314 \), we can analyze the situation using the properties of exponents.
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The expression \( 353 - 9 \) can be rewritten using the property of negative exponents. Specifically, \( 353 \) can be expressed as \( 3^{53} \), and when you subtract \( 9 \) from the exponent, it translates to \( 3^{53-9} \) which simplifies to \( 3^{44} \).
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The resulting expression \( 3^{44} \) does not relate to \( 314 \) unless we've made a mistake in assumptions or calculations.
So, in this specific case, it appears that we should be considering the properties involved:
- The Property of Negative Exponents allowed the conversion of subtraction in exponents into a negative exponent.
- The Product Rule of Exponents could relate to combining exponential bases if necessary (but isn't applicable here directly).
Given the options:
- only the Property of Negative Exponents: This is partially correct if we consider that exponent subtraction generally involves negative exponents.
- only the Product Rule of Exponents: This wouldn't apply here since we don't have a product situation to apply.
- only the Power Rule of Exponents: This isn't applicable as we aren't raising a power to another power.
- the Property of Negative Exponents and the Product Rule of Exponents: This suggests a combination, but again the latter isn't relevant here.
Considering the context, the best answer reflecting the reasoning appears to involve negative exponents applied—so the closest suitable option is:
Only the Property of Negative Exponents.
However, if the simplification \( 314 \) directly is indeed derived from exponent rules beyond what we see, clarification on original arithmetic would be necessary since \( 314 \) may suggest some direct multiplication by the base or additional steps not visible in the statement alone. If needed, ensure to clarify how \( 314 \) is formed if it truly is from exponents.