To determine the validity of the equation \( 10^{-13} = -10^{-\frac{1}{3}} \), we need to analyze both sides using the properties of exponents.
The left side is:
\[
10^{-13} = \frac{1}{10^{13}}.
\]
The right side can be rewritten using the Negative Exponent Rule:
\[
-10^{-\frac{1}{3}} = -\frac{1}{10^{\frac{1}{3}}}.
\]
This means the equation becomes:
\[
\frac{1}{10^{13}} = -\frac{1}{10^{\frac{1}{3}}}.
\]
Clearly, \( \frac{1}{10^{13}} \) is a positive number, while \( -\frac{1}{10^{\frac{1}{3}}} \) is a negative number. Thus, these two sides are not equal.
Therefore, the correct response is:
**False, because the Negative Exponent Rule requires that the number be rewritten as a quotient, not as a negative value.**