To solve the equation \(-x^{3/2} = -27\), we can first eliminate the negative signs from both sides:
\[ x^{3/2} = 27 \]
Next, to isolate \(x\), we can raise both sides to the power of \(\frac{2}{3}\):
\[ x = 27^{2/3} \]
We can rewrite \(27\) as \(3^3\), so we have:
\[ 27^{2/3} = (3^3)^{2/3} = 3^{3 \cdot \frac{2}{3}} = 3^2 = 9 \]
Thus, the solution is:
\[ x = 9 \]
None of the options given in your question include \(9\), however, \(x\) is positive, not negative. Thus, the correct interpretation based on the options provided would be:
- No solution, the answer cannot be negative.
If this selection implies the assumption that \(x\) must be negative, then it would be the most fitting option based on the given choices. However, mathematically, the actual solution is \(x = 9\).
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