1 answer
(click or scroll down)
To evaluate the equation \( 10^{-13} = -10^{-\sqrt{3}} \), we need to analyze both sides of the equation using the properties of exponents.
Starting with the left side:
\[
10^{-13} = \frac{1}{10^{13}}
\]
Now, let’s evaluate the right side.
The term \( -10^{-\sqrt{3}} \) can be rewritten as:
\[
-10^{-\sqrt{3}} = -\frac{1}{10^{\sqrt{3}}}
\]
Since \( \sqrt{3} \) is a positive number, \( 10^{\sqrt{3}} \) is also positive. Hence, \( -\frac{1}{10^{\sqrt{3}}} \) is a negative number.
Now we compare both sides:
- The left side \( 10^{-13} = \frac{1}{10^{13}} \) is a positive number.
- The right side \( -10^{-\sqrt{3}} = -\frac{1}{10^{\sqrt{3}}} \) is a negative number.
Since a positive number cannot equal a negative number, the equation \( 10^{-13} = -10^{-\sqrt{3}} \) is false.
Thus, the final answer is **False**.