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

Question

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

Answer 1

The property of exponents used to generate the equivalent expression is the quotient rule of exponents. According to the quotient rule, when dividing two exponential expressions with the same base, you subtract the exponents.

In this case, 3^5 divided by 3^9 can be simplified as 3^(5-9) = 3^-4.

To generate the equivalent expression, the negative exponent can be expressed as the reciprocal of the positive exponent.

Therefore, 3^-4 can be written as 1/3^4, which is equivalent to 3^14.

Answer 2

The property of exponents used to generate the equivalent expression 3^14 from 3^5/3^9 is the quotient property of exponents. According to this property, when dividing two numbers with the same base, you subtract the exponents. In this case, 3^5/3^9 can be rewritten as 3^(5-9) = 3^-4. By using the property of negative exponents, we can further rewrite it as 1/3^4. Finally, by simplifying 1/3^4, we get 3^14.