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 False, because according to the Negative Exponent Rule, the equation should be 10−13=−110√3. 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 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. True, because the negative sign moves to the front when writing an equivalent expression.

Answer 1

To determine whether the equation \(10^{-13} = -10^{-\frac{1}{3}}\) is true or false, we need to analyze both sides using the properties of exponents.

1. Evaluate the left side: \[ 10^{-13} = \frac{1}{10^{13}} \]

2. Evaluate the right side: \[ -10^{-\frac{1}{3}} = -\frac{1}{10^{\frac{1}{3}}} \]

Now we will compare both sides:

• The left side is a very small positive number (since when you take the reciprocal of a large number, you get a small number).
• The right side is a negative number (since it is negative one times a positive number).

Thus, since one side is positive and the other side is negative, the equation is clearly false.

The correct justification is:

False, because according to the Negative Exponent Rule, the equation should be \(10^{-13} = -\frac{1}{10^{\frac{1}{3}}}\), and the left side is positive while the right side is negative.