Which property of exponents was used to generate the equivalent expression 3^14 from 35^/3^−9?(1 point)
Responses
only the Power Rule of Exponents
only the Power Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
only the Product Rule of Exponents
only the Product Rule of Exponents
only the Property of Negative Exponents
The answer is: only the Property of Negative Exponents
The property of negative exponents and the product rule of exponents were used to generate the equivalent expression 3^14 from 35^/3^−9.
To generate the equivalent expression 3^14 from 35^(3^-9), we need to apply the Property of Negative Exponents and the Product Rule of Exponents.
First, let's apply the Property of Negative Exponents: when a term has a negative exponent, we can rewrite it as the reciprocal of the same term with the positive exponent. In this case, 3^(-9) can be rewritten as 1/(3^9).
Now, let's apply the Product Rule of Exponents: when two terms with the same base are multiplied together, we can add their exponents. In this case, we have 35 and (1/(3^9)) multiplied together. By applying the Product Rule of Exponents, we can rewrite it as 35 * (1/(3^9)) = 35/(3^9).
Finally, if we simplify 35/(3^9), we can rewrite it as 3^(14). Therefore, both the Property of Negative Exponents and the Product Rule of Exponents were used to generate the equivalent expression 3^14 from 35^(3^-9).