Final answer:
To generate 3¹⁴ from 3⁵/3⁻⁹, the property of negative exponents (to convert 3⁻⁹ into 1/3⁹) and the product rule (to add exponents 3⁵ * 3⁹) were used, leading to the answer of 3¹⁴. D) The property of negative exponents, and the product rule of exponents.
Step-by-step explanation:
To generate the equivalent expression 3¹⁴ from 3⁵/3⁻⁹, two properties of exponents are used: the property of negative exponents and the product rule of exponents. Using the property of negative exponents, 3⁻⁹ becomes 1/3⁹. When dividing exponents with the same base, you subtract the exponents: 3⁵ / (1/3⁹) which simplifies to 3⁵ * 3⁹ due to the fact that dividing by a fraction is equivalent to multiplying by its reciprocal. Applying the product rule of exponents, where you add the exponents when multiplying like bases, this further simplifies to 3¹⁴. The correct option is therefore D) The property of negative exponents, and the product rule of exponents.