The expression \( 35^3 - 9 \) doesn't seem to directly relate to exponent properties, but if we assume it's a typographical error and you're trying to simplify \( 35^3 - 35^9 \), we would focus on the properties of exponents.
To express \( 35^3 - 35^9 \) in a different way, we can apply the Property of Negative Exponents and the Product Rule of Exponents.
However, since you mentioned generating the expression \( 314 \), it seems there might be a misunderstanding or error in the expression provided.
If you meant to express something like \( 35^3 \) as an equivalent expression but resulted in \( 314 \), you didn't explicitly use a property of exponents, but rather might have intended to simplify \( 35^{-9} \) to involve a subtraction.
If we clarify that, the combination of Property of Negative Exponents (e.g., \( a^{-n} = \frac{1}{a^n} \)) and the Product Rule of Exponents could yield a specific form.
Thus, the most appropriate response given these assumptions would be:
- the Property of Negative Exponents and the Product Rule of Exponents.