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)ResponsesTrue, 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.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=−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 .True, because the Negative Exponent Rule requires that the number be rewritten as a negative value.

Question

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)ResponsesTrue, 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.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=−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 .True, because the Negative Exponent Rule requires that the number be rewritten as a negative value.

GPT-4o mini · Answer

To determine whether the equation $ 10^{-13} = -10^{-\frac{1}{3}} $ is true or false, let's analyze both sides: 1. **Left Side:** $$ 10^{-13} = \frac{1}{10^{13}} $$ 2. **Right Side:** $$ -10^{-\frac{1}{3}} = -\frac{1}{10^{\frac{1}{3}}} = -\frac{1}{\sqrt[3]{10}} $$ Now let’s simplify the expressions: - The left side $ 10^{-13} $ is a very small positive number (since it represents $ \frac{1}{10^{13}} $). - The right side $ -10^{-\frac{1}{3}} $ is a negative number (since it represents $ -\frac{1}{\sqrt[3]{10}} $). Since one side is positive and the other side is negative, the two sides cannot be equal. Thus, the equation $ 10^{-13} = -10^{-\frac{1}{3}} $ is **false**. Now, let’s look at the response options. The one that correctly answers the question and provides appropriate justification is: **False, because the Negative Exponent Rule requires that the number be rewritten as a quotient, not as a negative value.** This is indeed correct, but the key justification here is more about understanding that one side is positive and the other side is negative, which is the main reason they cannot be equal.