Which of the following is an equivalent expression to 81^−1/2
1. −81−−√
2. 181√
3. 81−−√
4. −181√
2. 181√
Use the properties of exponents to determine whether the equation 10−13=−10−−√3 is true or false. Select the response that correctly answers the question and provides the appropriate justification.(1 point)
Responses
True, because the negative sign moves to the front when writing an equivalent expression.
True, because the negative sign moves to the front when writing an equivalent expression.
True, because the Negative Exponent Rule requires that the number be rewritten as a negative value
True, because the Negative Exponent Rule requires that the number be rewritten as a negative value
False, because the Negative Exponent Rule requires that the number be rewritten as a quotient, not as a negative value.
False, because the Negative Exponent Rule requires that the number be rewritten as a quotient, not as a negative value.
False, because according to the Negative Exponent Rule, the equation should be 10^−13 = −1/10√3.
False, because the Negative Exponent Rule requires that the number be rewritten as a quotient, not as a negative value.
Use the properties of exponents to determine whether the equation 10^−1/3 = −10−−√3 is true or false. Select the response that correctly answers the question and provides the appropriate justification.(1 point)
Responses
True, because the negative sign moves to the front when writing an equivalent expression.
True, because the negative sign moves to the front when writing an equivalent expression.
True, because the Negative Exponent Rule requires that the number be rewritten as a negative value
True, because the Negative Exponent Rule requires that the number be rewritten as a negative value
False, because the Negative Exponent Rule requires that the number be rewritten as a quotient, not as a negative value.
False, because the Negative Exponent Rule requires that the number be rewritten as a quotient, not as a negative value.
False, because according to the Negative Exponent Rule, the equation should be 10^−13 = −1/10√3.
True, because the negative sign moves to the front when writing an equivalent expression.
Use the properties of exponents to determine whether the equation 10^−1/3 = −10−−√3 is true or false. Select the response that correctly answers the question and provides the appropriate justification.(1 point)
True, because the negative sign moves to the front when writing an equivalent expression.
True, because the Negative Exponent Rule requires that the number be rewritten as a negative value
False, because the Negative Exponent Rule requires that the number be rewritten as a quotient, not as a negative value.
False, because according to the Negative Exponent Rule, the equation should be 10^−13 = −1/10√3.
False, because according to the Negative Exponent Rule, the equation should be 10^(-1/3) = 1/(10^(1/3)), which is not equal to −10^(-√3).
Is the equation 3^−5 ⋅ (81√4)^3/3^−4 = 3^−6 true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)
Responses
1. False. There is an error in calculation using the Quotient Property.
2. True. All rules have been applied correctly.
3. True, but the equation should be simplified using the Negative Exponent Rule.
4. False. There is an error in applying the Product Property.
3. True, but the equation should be simplified using the Negative Exponent Rule.
To simplify the equation, we can start by applying the power of a quotient property:
(3^(-5)) * ((81√4)^(3/3)) / 3^(-4)
Next, we simplify the term (81√4)^(3/3):
(3^(-5)) * (81√4) * 3/3^(-4)
Then, we simplify further using the product property:
(3^(-5)) * (81√4) * 3 * 3^4
Finally, we use the Negative Exponent Rule to simplify 3^(-5) and 3^(-4):
(1/3^5) * (81√4) * 3 * (1/3^(-4))
Simplifying this expression gives us:
(1/243) * (81√4) * 3 * 81
Simplifying further:
(1/243) * 243 * 3 * 81
(1/1) * 3 * 81
3 * 81
243
Since 3^(-6) is equal to 1/3^6, and 1/3^6 is not equal to 243, the equation 3^(-5) * (81√4)^(3/3) / 3^(-4) = 3^(-6) is FALSE.