Which property of exponents was used to generate the equivalent expression 3^14 from 3^5/3^−9
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.
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
The correct answer is the Property of Negative Exponents and the Product Rule of Exponents.
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?
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).
The property that was used to generate the equivalent expression 3^14 from 3^5/3^−9 is the quotient of powers property.
According to the quotient of powers property, when dividing two powers with the same base, you subtract the exponents.
In this case, we have 3^5 divided by 3^−9. To simplify this expression using the quotient of powers property, we subtract the exponents:
3^5 / 3^−9 = 3^(5 - (-9))
Simplifying 5 - (-9) gives us:
3^14
So, the equivalent expression is 3^14.
To generate the equivalent expression 3^14 from 3^5/3^−9, the property of exponents that was used is the quotient rule.
The quotient rule states that when dividing two exponential expressions with the same base, you subtract the exponents. So, if you have a^m / a^n, where "a" is the base and "m" and "n" are exponents, you can simplify it as a^(m - n).
In this case, we have 3^5/3^−9. To apply the quotient rule, subtract the exponent of the denominator from the exponent of the numerator:
3^5 / 3^(-9) = 3^(5 - (-9))
When subtracting a negative number, it is the same as adding its positive counterpart:
3^(5 - (-9)) = 3^(5 + 9)
Now, you can add the exponents:
3^(5 + 9) = 3^14
So, the equivalent expression 3^14 is generated using the quotient rule of exponents.