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To solve the equation \(-x^{3/2} = -27\), we can first eliminate the negative signs on both sides:
\[
x^{3/2} = 27
\]
Next, we can raise both sides to the power of \(\frac{2}{3}\) to isolate \(x\):
\[
x = 27^{2/3}
\]
Now, we can simplify \(27^{2/3}\). The cube root of 27 is 3 (since \(3^3 = 27\)), and then we square it:
\[
27^{2/3} = (3)^2 = 9
\]
So the solution to the equation is:
\[
\boxed{9}
\]