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To determine whether the equation \( 10^{-1/3} = -10^{-\sqrt{3}} \) is true or false, we can simplify both sides of the equation.
1. **Left Side**:
\[
10^{-1/3} = \frac{1}{10^{1/3}} = \frac{1}{\sqrt[3]{10}}
\]
2. **Right Side**:
\[
-10^{-\sqrt{3}} = -\frac{1}{10^{\sqrt{3}}} = -\frac{1}{10^{\sqrt{3}}}
\]
Now, let’s compare the two results:
- The left side, \( 10^{-1/3} \), is positive because it is the reciprocal of a positive number.
- The right side, \( -10^{-\sqrt{3}} \), is negative because it is the negative of a positive number.
Since one side is positive and the other side is negative, we can conclude that:
**The equation \( 10^{-1/3} = -10^{-\sqrt{3}} \) is false.**