Which property of exponents was used to generate the equivalent expression 3^14 from 3^5 over 3^−9??

Question

options:

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

Answer 1

To generate the expression \( 3^{14} \) from \( \frac{3^5}{3^{-9}} \), we can use the Product Rule of Exponents.

The Product Rule states that when you divide two expressions with the same base, you subtract the exponents:

\[ \frac{a^m}{a^n} = a^{m-n} \]

Applying this rule to \( \frac{3^5}{3^{-9}} \):

\[ \frac{3^5}{3^{-9}} = 3^{5 - (-9)} = 3^{5 + 9} = 3^{14} \]

So, in this case, the key property used is the Product Rule of Exponents.

The correct answer is: only the Product Rule of Exponents.