Which property of exponents was used to generate the equivalent expression 3^14 from 3^5/3^−9 ?(1 point) Responses
the Property of Negative Exponents and the Product Rule of Exponents
only the Power Rule of Exponents
only the Property of Negative Exponents
only the Product Rule of Exponents
The Property of Negative Exponents and the Product Rule of Exponents were both used to generate the equivalent expression 3^14 from 3^5/3^−9.
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?(1 point)
To generate an equivalent expression with only positive exponents, we can use the Property of Negative Exponents and the Property of Division of Exponents.
Starting with the given expression:
15^0 ⋅ 7^−2/(−4)^−3
Using the Property of Negative Exponents to change the sign of the exponents:
1/15^0 ⋅ 1/7^2/1/(−4)^3
Simplifying the zero exponent and applying the Property of Division of Exponents:
1/1 ⋅ 1/(7^2 * −4^3)
Simplifying the exponent expressions:
1 / (1 * 49 * −64)
Combining the numerators and evaluating the expression:
1 / (-3136)
Therefore, the equivalent expression with only positive exponents is 1 / 3136.
Which of the following is an equivalent expression to 15⁰ ⋅ 7⁻² / (−4)⁻³ with only positive exponents that has been generated by applying the properties of integer exponents?
a. 1/ (7² . (-4)⁻³)
b. (-4)³ / 7²
c. 7² / (-4)³
d. 4³ / 7²
To generate an equivalent expression with only positive exponents, we can use the properties of integer exponents:
Starting with the given expression: 15⁰ ⋅ 7⁻² / (−4)⁻³
Using the property of negative exponents to change the sign of the exponents:
1/15⁰ ⋅ 1/7² / 1/(−4)³
Simplifying the zero exponent:
1/1 ⋅ 1/49 / 1/(−64)
Simplifying the division of exponents:
1 / (49 * −64)
Simplifying the expression:
1 / (-3136)
Therefore, the equivalent expression with only positive exponents is 1 / 3136.
The correct answer is not listed among the options provided, as none of them correspond to the equivalent expression obtained.