To solve the equation \(-x^{2.9} = -3\), we can first eliminate the negative sign from both sides:
\[ x^{2.9} = 3 \]
Next, we take both sides to the power of \(\frac{1}{2.9}\):
\[ x = 3^{\frac{1}{2.9}} \]
Now we can calculate \(3^{\frac{1}{2.9}}\). Using a calculator:
\[ 3^{\frac{1}{2.9}} \approx 1.5157 \]
Since \(x\) can be either positive or negative, the solutions to the equation are:
\[ x \approx 1.5157 \quad \text{and} \quad x \approx -1.5157 \]
Now, let's look at the provided options: \(8.7\), \(-87\), \(-8.7\), \(87\).
None of these options are close to \(1.5157\) or \(-1.5157\). Let's recheck the calculations.
- Calculate \(3^{1/2.9}\): \[ 3^{1/2.9} \approx 1.5157 , (which is valid) \]
Now, realizing there's a misunderstanding in matching the exact values to the choices given, it seems none of the options correspond to the correct value derived from the equation.
Thus, the correct numerical solution \(x \approx \pm 1.5157\) does not match any of the answers provided, as the closest potential answers do not line up.
In conclusion, the solution does not correspond with the options available.