Which property of exponents was used to generate the equivalent expression 3^14 from 3^5/3^-9?
The property of negative exponents and the product rule of exponents
Only the power rule of exponents
Only the product rule of exponents
Only the property of negative exponents
Only the product rule of exponents
The property of negative exponents is used in this case to generate the equivalent expression 3^14 from 3^5/3^-9.
The property of negative exponents and the product rule of exponents were used to generate the equivalent expression 3^14 from 3^5/3^-9.
To understand how the transformation was done, let's break it down step by step:
1. Start with the original expression 3^5/3^-9.
2. Apply the property of negative exponents, which states that any term with a negative exponent can be moved to the denominator by changing the sign of the exponent. In this case, the 3^-9 term becomes 1/3^9.
3. After applying the property of negative exponents, we now have 3^5/(1/3^9).
4. Next, apply the product rule of exponents, which states that when dividing two exponential terms with the same base, we can subtract their exponents. In this case, 3^5 / (1/3^9) becomes 3^(5 + 9).
5. Finally, simplify the exponent by adding 5 + 9, which gives us 3^14.
So, both the property of negative exponents and the product rule of exponents were used in this transformation, making the correct answer: "The property of negative exponents and the product rule of exponents."