Use the properties of exponents to determine whether the equation 10−13=−10−−√3

Question

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 .

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.

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.
Skip to navigation

Answer 1

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

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

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

Now we have:

• Left side: \( \frac{1}{10^{13}} \)
• Right side: \( -\frac{1}{10^{\sqrt{3}}} \)

To compare these, it's clear that the left side is a positive number (since \( 10^{13} \) is positive and thus \( \frac{1}{10^{13}} \) is positive), whereas the right side is negative (since it starts with a negative sign). Therefore, these two values cannot be equal.

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.