Question

Use the properties of exponents to determine whether the equation 10^-1/3 =-3√10
is true or false. Select the response that correctly answers the question and provides the appropriate justification.(1 point)
Responses

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 according to the Negative Exponent Rule, the equation should be 10^−1/3=−1/3√10
.
False, because according to the Negative Exponent Rule, the equation should be 10 superscript negative Start Fraction 1 over 3 End Fraction baseline equals negative Start Fraction 1 over root index 3 Start Root 10 End Root End Fraction .

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.

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.

Answer 1

False — because a negative exponent means take the reciprocal, not make the value negative. 10^(−1/3) = 1/(10^(1/3)) = 1/∛10, which is not −∛10 (or −3√10). So the correct response is: "False, because the Negative Exponent Rule requires that the number be rewritten as a quotient, not as a negative value."