Which property of exponents was used to generate the equivalent expression 3^14 from 3^5/3^-9?
1. only the Product Rule Of Exponents
2. only the Property of Negative Exponents
3. the Property of Negative and the Product Rule of Exponents
4. Only the Power Rule of Exponents
The property of negative exponents was used to generate the equivalent expression 3^14 from 3^5/3^-9.
Thus, the correct answer is 2. only the Property of Negative Exponents.
The correct answer is 3. The Property of Negative and the Product Rule of Exponents were both used to generate the equivalent expression 3^14 from 3^5/3^-9.
To generate the equivalent expression 3^14 from 3^5/3^-9, we need to understand and apply the properties of exponents. Let's look at the options provided:
1. The Product Rule of Exponents states that when multiplying powers with the same base, you add their exponents. However, in the given expression 3^5/3^-9, there is a division, not a multiplication. Therefore, this rule is not directly applicable.
2. The Property of Negative Exponents states that any nonzero number raised to a negative exponent is equal to one divided by the same number raised to the positive exponent. In the given expression, 3^-9 can be rewritten as 1/3^9. However, this property alone doesn't lead to the equivalent expression 3^14.
3. The Property of Negative Exponents and the Product Rule of Exponents together can be used to solve the equation. As mentioned earlier, 3^-9 can be rewritten as 1/3^9. Now, when you divide 3^5 by 1/3^9, you can apply the Product Rule of Exponents, which states that dividing powers with the same base is equivalent to subtracting their exponents. This gives us 3^14 as the final equivalent expression. Therefore, option 3 is correct.
4. The Power Rule of Exponents states that when raising a power to another power, you multiply the exponents. However, in the given expression, there is no power to another power. Hence, option 4 is not applicable.
In conclusion, the correct answer is option 3: the Property of Negative and the Product Rule of Exponents.