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

Answer 1

The property of exponents that was used to generate the equivalent expression is the quotient property of exponents. According to this property, when dividing two exponential expressions with the same base, you subtract the exponents from each other. Therefore, 3^5/3^-9 can be rewritten as 3^(5-(-9)), which simplifies to 3^14.

Answer 2

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

only the Product Rule of Exponents
only the Product Rule of Exponents

only the Power Rule of Exponents
only the Power Rule of Exponents

the Property of Negative Exponents and the Product Rule of Exponents

Answer 3

The correct answer is the Property of Negative Exponents and the Product Rule of Exponents.

Answer 4

Which of the following is an equivalent expression to 15^0 ⋅ 7^−2 (−4)^−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?

Answer 5

To simplify the expression 15^0 ⋅ 7^−2 (−4)^−3 with only positive exponents, we can use the property of exponents, which states that any non-zero number raised to the power of 0 is equal to 1. Additionally, we can use the property of negative exponents, which states that any number raised to a negative exponent can be rewritten as the reciprocal of the number raised to the positive value of the exponent.

Therefore, to simplify the expression, we have:

15^0 ⋅ 7^−2 (−4)^−3
= 1 ⋅ (1/7^2) ⋅ (1/(-4)^3)
= (1/1) ⋅ (1/49) ⋅ (1/(-64))
= 1/(-3136)

So, an equivalent expression with only positive exponents is 1/(-3136).