Which property of exponents was used to generate the equivalent expression 3^14 from 3^5/3^−9?
only the Property of Negative Exponents
only the Property of Negative Exponents
the Property of Negative Exponents and the Product Rule of Exponents
the Property of Negative Exponents and the Product
Rule of Exponents
which
The correct answer is "the Property of Negative Exponents and the Product Rule of Exponents".
The property of exponents used to generate the equivalent expression 3^14 from 3^5/3^−9 is the property of negative exponents.
To generate the equivalent expression 3^14 from 3^5/3^−9, we need to use the Property of Negative Exponents and the Product Rule of Exponents. Let's break it down:
1. Property of Negative Exponents: When a base with a negative exponent is in the denominator, it can be moved to the numerator by changing the sign of the exponent. In this case, 3^−9 can be rewritten as 1/3^9.
2. Product Rule of Exponents: When dividing two exponential expressions with the same base, you subtract the exponents. In this case, 3^5/1/3^9 can be rewritten as 3^5 * 3^−9.
Now, we can combine these two properties:
3^5 * 3^−9 = 3^(5 + −9) = 3^(-4) = 1/3^4
Finally, we simplify 1/3^4 to get the equivalent expression: 3^14.