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.**